TY  - JOUR
AU  - Mutavdžić Đukić, Rada
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3742
AB  - In this paper we analyze the generalized averaged Gaussian quadrature formulas and the simplest truncated variant for one of them for some weight functions on the interval [0, 1] considered by Milovanovic in [10]. We shall investigate internality of these formulas for the equivalents of the Jacobi polynomials on this interval and, in some special cases, show the existence of the Gauss-Kronrod quadrature formula. We also include some examples showing the corresponding error estimates for some non-classical orthogonal polynomials.
PB  - Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac
T2  - Kragujevac Journal of Mathematics
T1  - Generalized averaged gaussian formulas for certain weight functions
EP  - 305
IS  - 2
SP  - 295
VL  - 46
DO  - 10.46793/KgJMat2202.295M
ER  - 

@article{
author = "Mutavdžić Đukić, Rada",
year = "2022",
abstract = "In this paper we analyze the generalized averaged Gaussian quadrature formulas and the simplest truncated variant for one of them for some weight functions on the interval [0, 1] considered by Milovanovic in [10]. We shall investigate internality of these formulas for the equivalents of the Jacobi polynomials on this interval and, in some special cases, show the existence of the Gauss-Kronrod quadrature formula. We also include some examples showing the corresponding error estimates for some non-classical orthogonal polynomials.",
publisher = "Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac",
journal = "Kragujevac Journal of Mathematics",
title = "Generalized averaged gaussian formulas for certain weight functions",
pages = "305-295",
number = "2",
volume = "46",
doi = "10.46793/KgJMat2202.295M"
}

Mutavdžić Đukić, R.. (2022). Generalized averaged gaussian formulas for certain weight functions. in Kragujevac Journal of Mathematics
Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac., 46(2), 295-305.
https://doi.org/10.46793/KgJMat2202.295M

Mutavdžić Đukić R. Generalized averaged gaussian formulas for certain weight functions. in Kragujevac Journal of Mathematics. 2022;46(2):295-305.
doi:10.46793/KgJMat2202.295M .

Mutavdžić Đukić, Rada, "Generalized averaged gaussian formulas for certain weight functions" in Kragujevac Journal of Mathematics, 46, no. 2 (2022):295-305,
https://doi.org/10.46793/KgJMat2202.295M . .

TY  - JOUR
AU  - Jandrlić, Davorka
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3782
AB  - In this paper, we consider the Kronrod extension for the Gauss-Radau and Gauss-Lobatto quadrature consisting of any one of the four Chebyshev weights. The main purpose is to effectively estimate the error of these quadrature formulas. This estimate needs a calculation of the maximum of the modulus of the kernel. We compute explicitly the kernel function and determine the locations on the ellipses where a maximum modulus of the kernel is attained. Based on this, we derive effective error bounds of the Kronrod extensions if the integrand is an analytic function inside of a region bounded by a confocal ellipse that contains the interval of integration.
PB  - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2  - Filomat
T1  - The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights
EP  - 977
IS  - 3
SP  - 961
VL  - 36
DO  - 10.2298/FIL2203961J
ER  - 

@article{
author = "Jandrlić, Davorka and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2022",
abstract = "In this paper, we consider the Kronrod extension for the Gauss-Radau and Gauss-Lobatto quadrature consisting of any one of the four Chebyshev weights. The main purpose is to effectively estimate the error of these quadrature formulas. This estimate needs a calculation of the maximum of the modulus of the kernel. We compute explicitly the kernel function and determine the locations on the ellipses where a maximum modulus of the kernel is attained. Based on this, we derive effective error bounds of the Kronrod extensions if the integrand is an analytic function inside of a region bounded by a confocal ellipse that contains the interval of integration.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights",
pages = "977-961",
number = "3",
volume = "36",
doi = "10.2298/FIL2203961J"
}

Jandrlić, D., Pejčev, A.,& Spalević, M.. (2022). The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 36(3), 961-977.
https://doi.org/10.2298/FIL2203961J

Jandrlić D, Pejčev A, Spalević M. The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights. in Filomat. 2022;36(3):961-977.
doi:10.2298/FIL2203961J .

Jandrlić, Davorka, Pejčev, Aleksandar, Spalević, Miodrag, "The Error Estimates of Kronrod Extension for Gauss-Radau and Gauss-Lobatto Quadrature with the Four Chebyshev Weights" in Filomat, 36, no. 3 (2022):961-977,
https://doi.org/10.2298/FIL2203961J . .

TY  - THES
AU  - Mutavdžić Đukić, Rada
PY  - 2020
UR  - http://eteze.kg.ac.rs/application/showtheses?thesesId=7543
UR  - https://fedorakg.kg.ac.rs/fedora/get/o:1259/bdef:Content/download
UR  - https://nardus.mpn.gov.rs/handle/123456789/17540
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/74
PB  - Univerzitet u Kragujevcu, Prirodno-matematički fakultet
T1  - Ocena greške u standardnim kvadraturama i kvadraturama za Furijeove koeficijente Gausovog tipa
UR  - https://hdl.handle.net/21.15107/rcub_nardus_17540
ER  - 

@phdthesis{
author = "Mutavdžić Đukić, Rada",
year = "2020",
publisher = "Univerzitet u Kragujevcu, Prirodno-matematički fakultet",
title = "Ocena greške u standardnim kvadraturama i kvadraturama za Furijeove koeficijente Gausovog tipa",
url = "https://hdl.handle.net/21.15107/rcub_nardus_17540"
}

Mutavdžić Đukić, R.. (2020). Ocena greške u standardnim kvadraturama i kvadraturama za Furijeove koeficijente Gausovog tipa. 
Univerzitet u Kragujevcu, Prirodno-matematički fakultet..
https://hdl.handle.net/21.15107/rcub_nardus_17540

Mutavdžić Đukić R. Ocena greške u standardnim kvadraturama i kvadraturama za Furijeove koeficijente Gausovog tipa. 2020;.
https://hdl.handle.net/21.15107/rcub_nardus_17540 .

Mutavdžić Đukić, Rada, "Ocena greške u standardnim kvadraturama i kvadraturama za Furijeove koeficijente Gausovog tipa" (2020),
https://hdl.handle.net/21.15107/rcub_nardus_17540 .

TY  - JOUR
AU  - Spalević, Miodrag
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3298
AB  - In the recent paper Notaris (Numer. Math., 142:129-147,2019) it has been introduced a new and useful class of nonnegative measures for which the well-known Gauss-Kronrod quadrature formulae coincide with the generalized averaged Gaussian quadrature formulas. In such a case, the given generalized averaged Gaussian quadrature formulas are of the higher degree of precision, and can be numerically constructed by an effective and simple method; see Spalevic (Math. Comp., 76:1483-1492,2007). Moreover, as almost immediate consequence of our results from Spalevic (Math. Comp.,76:1483-1492,2007) and that theory, we prove the main statements in Notaris (Numer. Math.,142:129-147,2019) in a different manner, by means of the Jacobi tridiagonal matrix approach.
PB  - Springer, Dordrecht
T2  - Numerical Algorithms
T1  - A note on generalized averaged Gaussian formulas for a class of weight functions
EP  - 993
IS  - 3
SP  - 977
VL  - 85
DO  - 10.1007/s11075-019-00848-x
ER  - 

@article{
author = "Spalević, Miodrag",
year = "2020",
abstract = "In the recent paper Notaris (Numer. Math., 142:129-147,2019) it has been introduced a new and useful class of nonnegative measures for which the well-known Gauss-Kronrod quadrature formulae coincide with the generalized averaged Gaussian quadrature formulas. In such a case, the given generalized averaged Gaussian quadrature formulas are of the higher degree of precision, and can be numerically constructed by an effective and simple method; see Spalevic (Math. Comp., 76:1483-1492,2007). Moreover, as almost immediate consequence of our results from Spalevic (Math. Comp.,76:1483-1492,2007) and that theory, we prove the main statements in Notaris (Numer. Math.,142:129-147,2019) in a different manner, by means of the Jacobi tridiagonal matrix approach.",
publisher = "Springer, Dordrecht",
journal = "Numerical Algorithms",
title = "A note on generalized averaged Gaussian formulas for a class of weight functions",
pages = "993-977",
number = "3",
volume = "85",
doi = "10.1007/s11075-019-00848-x"
}

Spalević, M.. (2020). A note on generalized averaged Gaussian formulas for a class of weight functions. in Numerical Algorithms
Springer, Dordrecht., 85(3), 977-993.
https://doi.org/10.1007/s11075-019-00848-x

Spalević M. A note on generalized averaged Gaussian formulas for a class of weight functions. in Numerical Algorithms. 2020;85(3):977-993.
doi:10.1007/s11075-019-00848-x .

Spalević, Miodrag, "A note on generalized averaged Gaussian formulas for a class of weight functions" in Numerical Algorithms, 85, no. 3 (2020):977-993,
https://doi.org/10.1007/s11075-019-00848-x . .

TY  - JOUR
AU  - Orive, Ramon
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3401
AB  - In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of each of the four Chebyshev weights, considered by Gautschi and Li in [4]. As it is well known, in the case of analytic integrands the error of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel of the mentioned quadrature formulas on suitable elliptic contours, in such a way that the behavior of its modulus is analyzed in a rather simple manner, allowing us to derive some effective error bounds. In addition, some numerical examples checking the accuracy of such error bounds are included.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematics and Computation
T1  - The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type
VL  - 369
DO  - 10.1016/j.amc.2019.124806
ER  - 

@article{
author = "Orive, Ramon and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2020",
abstract = "In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of each of the four Chebyshev weights, considered by Gautschi and Li in [4]. As it is well known, in the case of analytic integrands the error of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel of the mentioned quadrature formulas on suitable elliptic contours, in such a way that the behavior of its modulus is analyzed in a rather simple manner, allowing us to derive some effective error bounds. In addition, some numerical examples checking the accuracy of such error bounds are included.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematics and Computation",
title = "The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type",
volume = "369",
doi = "10.1016/j.amc.2019.124806"
}

Orive, R., Pejčev, A.,& Spalević, M.. (2020). The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type. in Applied Mathematics and Computation
Elsevier Science Inc, New York., 369.
https://doi.org/10.1016/j.amc.2019.124806

Orive R, Pejčev A, Spalević M. The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type. in Applied Mathematics and Computation. 2020;369.
doi:10.1016/j.amc.2019.124806 .

Orive, Ramon, Pejčev, Aleksandar, Spalević, Miodrag, "The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type" in Applied Mathematics and Computation, 369 (2020),
https://doi.org/10.1016/j.amc.2019.124806 . .

TY  - THES
AU  - Tomanović, Jelena
PY  - 2019
UR  - http://eteze.kg.ac.rs/application/showtheses?thesesId=7025
UR  - https://nardus.mpn.gov.rs/handle/123456789/11718
UR  - https://fedorakg.kg.ac.rs/fedora/get/o:1168/bdef:Content/download
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/68
AB  - Numeriqka integracija prouqava kako se moe izraqunati brojevna vrednost integrala. Formule numeriqke integracije nazivaju se  kvadraturama. Jedinstvena optimalna interpolaciona kvadratura sa  n qvorova jeste Gausova formula Gn, koja ima algebarski stepen taqnosti 2n−1. Vano pitanje u praktiqnim izraqunavanjima je kako (ekonomiqno) proceniti grexku Gausove formule. U te svrhe moe se koristiti odgovarajua Gaus-Kronrodova formula K2n+1 sa 2n+1 qvorova i algebarskim stepenom taqnosti 3n+1. U situacijam kada Gaus-Kronrodova formula ne postoji, treba nai adekvatnu alternativu i ta alternativa moe biti uopxtena usrednjena Gausova formula Gb2n+1 sa  2n + 1 qvorova i algebarskim stepenom taqnosti 2n + 2. Prednosti  Gb2n+1 su to xto uvek postoji i to xto je njena numeriqka konstrukcija  jednostavnija od konstrukcije K2n+1.  Glavna tema ove doktorske disertacije je uopxtena usrednjena Gausova formula Gb2n+1.  Uopxtene usrednjene Gausove formule mogu imati qvorove van intervala integracije. Kvadrature sa qvorovima van intervala integracije ne mogu se koristiti za aproksimaciju integrala kod kojih je  integrand definisan samo na intervalu integracije. U ovoj disertaciji ispitano je kada uopxtene usrednjene Gausove formule i njihova  skraenja sa Bernxtajn-Segeovim teinskim funkcijama imaju sve qvorove unutar intervala integracije.  Neki integrali po m-dimenzionalnim oblastima mogu se aproksimirati formulama Gm n konstruisanim uzastopnom primenom Gausovih  kvadratura Gn. Koristei odgovarajue Gaus-Kronrodove kvadrature  K2n+1 ili odgovarajue uopxtene usrednjene Gausove kvadrature Gb2n+1  umesto Gn, u ovoj disertaciji konstruixemo formule K2mn+1 i Gbm 2n+1.  Kako bismo procenili grexku jIm − Gm n j koristimo razlike jK2mn+1 −  Gm  n j i jGbm 2n+1 − Gm n j. Razmatramo integrale po m-dimenzionalnoj kocki,  simpleksu, sferi i lopti.
AB  - Numerical integration is the study of how numerical value of an integral can  be calculated. Formulas for numerical integration are called quadrature rules. The unique optimal interpolatory quadrature rule with n nodes is Gauss formula Gn, which has algebraic degree os exactness 2n − 1. An important task in practical  calculations is how to (economically) estimate the error of Gauss formula. For  this purpose corresponding Gauss-Kronrod formula K2n+1 with 2n + 1 nodes and  algebraic degree of exactness 3n + 1 can be used. In the situations when GaussKronrod formula doesn’t exist, it is of interest to find adequate alternative and  this alternative can be corresponding generalized averaged Gauss formula Gb2n+1  with 2n + 1 nodes and algebraic degree of exactness 2n + 2. The adventages of  Gb2n+1 are that it always exists, and that it’s numerical construction is simpler  than the construction of K2n+1.  The principal topic of this doctoral dissertation is generalized averaged Gauss  formula Gb2n+1.  Generalized averaged Gauss formulas may have nodes outside the interval  of integration. Quadrature rules with nodes outside the interval of integration  cannot be applied to approximate integrals with an integrand that is defined on  the interval of integration only. This thesis investigates when generalized averaged  Gauss formulas and their truncations for Bernstein-Szeg˝o weight functions have  all nodes in the interval of integration.  Some integrals Im over m-dimensional regions can be approximated by cubature formulas Gm  n constructed by the product of Gauss quadrature rules Gn. Using  corresponding Gauss-Kronrod rules K2n+1 or corresponding generalized averaged  Gauss rules Gb2n+1 instead of Gn, in this thesis we construct cubature formulas  Km  2n+1 and Gbm 2n+1. In order to estimate the error jIm − Gm n j we use the differences  jK2mn+1 − Gm n j and jGbm 2n+1 − Gm n j. We consider integrals over m-dimensional cube,  simplex, sphere and ball.
PB  - Univerzitet u Kragujevcu, Prirodno-matematički fakultet
T1  - Usrednjene kvadraturne formule sa varijantama i primene
T1  - Averaged quadrature formulas and vatiants with applications
UR  - https://hdl.handle.net/21.15107/rcub_nardus_11718
ER  - 

@phdthesis{
author = "Tomanović, Jelena",
year = "2019",
abstract = "Numeriqka integracija prouqava kako se moe izraqunati brojevna vrednost integrala. Formule numeriqke integracije nazivaju se  kvadraturama. Jedinstvena optimalna interpolaciona kvadratura sa  n qvorova jeste Gausova formula Gn, koja ima algebarski stepen taqnosti 2n−1. Vano pitanje u praktiqnim izraqunavanjima je kako (ekonomiqno) proceniti grexku Gausove formule. U te svrhe moe se koristiti odgovarajua Gaus-Kronrodova formula K2n+1 sa 2n+1 qvorova i algebarskim stepenom taqnosti 3n+1. U situacijam kada Gaus-Kronrodova formula ne postoji, treba nai adekvatnu alternativu i ta alternativa moe biti uopxtena usrednjena Gausova formula Gb2n+1 sa  2n + 1 qvorova i algebarskim stepenom taqnosti 2n + 2. Prednosti  Gb2n+1 su to xto uvek postoji i to xto je njena numeriqka konstrukcija  jednostavnija od konstrukcije K2n+1.  Glavna tema ove doktorske disertacije je uopxtena usrednjena Gausova formula Gb2n+1.  Uopxtene usrednjene Gausove formule mogu imati qvorove van intervala integracije. Kvadrature sa qvorovima van intervala integracije ne mogu se koristiti za aproksimaciju integrala kod kojih je  integrand definisan samo na intervalu integracije. U ovoj disertaciji ispitano je kada uopxtene usrednjene Gausove formule i njihova  skraenja sa Bernxtajn-Segeovim teinskim funkcijama imaju sve qvorove unutar intervala integracije.  Neki integrali po m-dimenzionalnim oblastima mogu se aproksimirati formulama Gm n konstruisanim uzastopnom primenom Gausovih  kvadratura Gn. Koristei odgovarajue Gaus-Kronrodove kvadrature  K2n+1 ili odgovarajue uopxtene usrednjene Gausove kvadrature Gb2n+1  umesto Gn, u ovoj disertaciji konstruixemo formule K2mn+1 i Gbm 2n+1.  Kako bismo procenili grexku jIm − Gm n j koristimo razlike jK2mn+1 −  Gm  n j i jGbm 2n+1 − Gm n j. Razmatramo integrale po m-dimenzionalnoj kocki,  simpleksu, sferi i lopti., Numerical integration is the study of how numerical value of an integral can  be calculated. Formulas for numerical integration are called quadrature rules. The unique optimal interpolatory quadrature rule with n nodes is Gauss formula Gn, which has algebraic degree os exactness 2n − 1. An important task in practical  calculations is how to (economically) estimate the error of Gauss formula. For  this purpose corresponding Gauss-Kronrod formula K2n+1 with 2n + 1 nodes and  algebraic degree of exactness 3n + 1 can be used. In the situations when GaussKronrod formula doesn’t exist, it is of interest to find adequate alternative and  this alternative can be corresponding generalized averaged Gauss formula Gb2n+1  with 2n + 1 nodes and algebraic degree of exactness 2n + 2. The adventages of  Gb2n+1 are that it always exists, and that it’s numerical construction is simpler  than the construction of K2n+1.  The principal topic of this doctoral dissertation is generalized averaged Gauss  formula Gb2n+1.  Generalized averaged Gauss formulas may have nodes outside the interval  of integration. Quadrature rules with nodes outside the interval of integration  cannot be applied to approximate integrals with an integrand that is defined on  the interval of integration only. This thesis investigates when generalized averaged  Gauss formulas and their truncations for Bernstein-Szeg˝o weight functions have  all nodes in the interval of integration.  Some integrals Im over m-dimensional regions can be approximated by cubature formulas Gm  n constructed by the product of Gauss quadrature rules Gn. Using  corresponding Gauss-Kronrod rules K2n+1 or corresponding generalized averaged  Gauss rules Gb2n+1 instead of Gn, in this thesis we construct cubature formulas  Km  2n+1 and Gbm 2n+1. In order to estimate the error jIm − Gm n j we use the differences  jK2mn+1 − Gm n j and jGbm 2n+1 − Gm n j. We consider integrals over m-dimensional cube,  simplex, sphere and ball.",
publisher = "Univerzitet u Kragujevcu, Prirodno-matematički fakultet",
title = "Usrednjene kvadraturne formule sa varijantama i primene, Averaged quadrature formulas and vatiants with applications",
url = "https://hdl.handle.net/21.15107/rcub_nardus_11718"
}

Tomanović, J.. (2019). Usrednjene kvadraturne formule sa varijantama i primene. 
Univerzitet u Kragujevcu, Prirodno-matematički fakultet..
https://hdl.handle.net/21.15107/rcub_nardus_11718

Tomanović J. Usrednjene kvadraturne formule sa varijantama i primene. 2019;.
https://hdl.handle.net/21.15107/rcub_nardus_11718 .

Tomanović, Jelena, "Usrednjene kvadraturne formule sa varijantama i primene" (2019),
https://hdl.handle.net/21.15107/rcub_nardus_11718 .

TY  - JOUR
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3012
AB  - Three kinds of effective error bounds of the quadrature formulas with multiple nodes that are generalizations of the well-known Micchelli-Rivlin quadrature formula, when the integrand is a function analytic in the regions bounded by confocal ellipses, are given. A numerical example which illustrates the calculation of these error bounds is included.
PB  - Science Press, Beijing
T2  - Science China-Mathematics
T1  - Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions
EP  - 1668
IS  - 9
SP  - 1657
VL  - 62
DO  - 10.1007/s11425-016-9259-5
ER  - 

@article{
author = "Pejčev, Aleksandar and Spalević, Miodrag",
year = "2019",
abstract = "Three kinds of effective error bounds of the quadrature formulas with multiple nodes that are generalizations of the well-known Micchelli-Rivlin quadrature formula, when the integrand is a function analytic in the regions bounded by confocal ellipses, are given. A numerical example which illustrates the calculation of these error bounds is included.",
publisher = "Science Press, Beijing",
journal = "Science China-Mathematics",
title = "Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions",
pages = "1668-1657",
number = "9",
volume = "62",
doi = "10.1007/s11425-016-9259-5"
}

Pejčev, A.,& Spalević, M.. (2019). Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions. in Science China-Mathematics
Science Press, Beijing., 62(9), 1657-1668.
https://doi.org/10.1007/s11425-016-9259-5

Pejčev A, Spalević M. Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions. in Science China-Mathematics. 2019;62(9):1657-1668.
doi:10.1007/s11425-016-9259-5 .

Pejčev, Aleksandar, Spalević, Miodrag, "Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions" in Science China-Mathematics, 62, no. 9 (2019):1657-1668,
https://doi.org/10.1007/s11425-016-9259-5 . .

TY  - JOUR
AU  - Mutavdžić Đukić, Rada
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3037
AB  - In this paper, we consider the Gauss-Lobatto quadrature formulas for the Bernstein-Szego weights, i.e., any of the four Chebyshev weights divided by a polynomial of the form rho(t) = 1 - 4 gamma/(1+gamma)(2) t(2), where t is an element of (-1,1) and gamma is an element of (-1,0]. Our objective is to study the kernel in the contour integral representation of the remainder term and to locate the points on elliptic contours where the modulus of the kernel is maximal. We use this to derive the error bounds for mentioned quadrature formulas.
PB  - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
T2  - Applicable Analysis and Discrete Mathematics
T1  - The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type
EP  - 745
IS  - 3
SP  - 733
VL  - 13
DO  - 10.2298/AADM190315030M
ER  - 

@article{
author = "Mutavdžić Đukić, Rada and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2019",
abstract = "In this paper, we consider the Gauss-Lobatto quadrature formulas for the Bernstein-Szego weights, i.e., any of the four Chebyshev weights divided by a polynomial of the form rho(t) = 1 - 4 gamma/(1+gamma)(2) t(2), where t is an element of (-1,1) and gamma is an element of (-1,0]. Our objective is to study the kernel in the contour integral representation of the remainder term and to locate the points on elliptic contours where the modulus of the kernel is maximal. We use this to derive the error bounds for mentioned quadrature formulas.",
publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd",
journal = "Applicable Analysis and Discrete Mathematics",
title = "The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type",
pages = "745-733",
number = "3",
volume = "13",
doi = "10.2298/AADM190315030M"
}

Mutavdžić Đukić, R., Pejčev, A.,& Spalević, M.. (2019). The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type. in Applicable Analysis and Discrete Mathematics
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 13(3), 733-745.
https://doi.org/10.2298/AADM190315030M

Mutavdžić Đukić R, Pejčev A, Spalević M. The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type. in Applicable Analysis and Discrete Mathematics. 2019;13(3):733-745.
doi:10.2298/AADM190315030M .

Mutavdžić Đukić, Rada, Pejčev, Aleksandar, Spalević, Miodrag, "The error bounds of gauss-lobatto quadratures for weights ofbernstein-szego type" in Applicable Analysis and Discrete Mathematics, 13, no. 3 (2019):733-745,
https://doi.org/10.2298/AADM190315030M . .

TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Orive, Ramon
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3157
AB  - Gaussian quadrature formulas, relative to the Chebyshev weight functions, with multiple nodes and their optimal extensions for computing the Fourier coefficients in expansions of functions with respect to a given system of orthogonal polynomials, are considered. The existence and uniqueness of such quadratures is proved. One of them is a generalization of the well-known Micchelli-Rivlin quadrature formula. The others are new. A numerically stable construction of these quadratures is proposed. By determining the absolute value of the difference between these Gaussian quadratures with multiple nodes for the Fourier-Chebyshev coefficients and their corresponding optimal extensions, we get the well-known methods for estimating their error. Numerical results are included. These results are a continuation of the recent ones in Bojanov & Petrova (2009, J. Comput. Appl. Math., 231, 378-391) and Milovanovic & Spalevic (2014, Math. Comput., 83, 1207-1231).
PB  - Oxford Univ Press, Oxford
T2  - Ima Journal of Numerical Analysis
T1  - Quadratures with multiple nodes for Fourier-Chebyshev coefficients
EP  - 296
IS  - 1
SP  - 271
VL  - 39
DO  - 10.1093/imanum/drx067
ER  - 

@article{
author = "Milovanović, Gradimir V. and Orive, Ramon and Spalević, Miodrag",
year = "2019",
abstract = "Gaussian quadrature formulas, relative to the Chebyshev weight functions, with multiple nodes and their optimal extensions for computing the Fourier coefficients in expansions of functions with respect to a given system of orthogonal polynomials, are considered. The existence and uniqueness of such quadratures is proved. One of them is a generalization of the well-known Micchelli-Rivlin quadrature formula. The others are new. A numerically stable construction of these quadratures is proposed. By determining the absolute value of the difference between these Gaussian quadratures with multiple nodes for the Fourier-Chebyshev coefficients and their corresponding optimal extensions, we get the well-known methods for estimating their error. Numerical results are included. These results are a continuation of the recent ones in Bojanov & Petrova (2009, J. Comput. Appl. Math., 231, 378-391) and Milovanovic & Spalevic (2014, Math. Comput., 83, 1207-1231).",
publisher = "Oxford Univ Press, Oxford",
journal = "Ima Journal of Numerical Analysis",
title = "Quadratures with multiple nodes for Fourier-Chebyshev coefficients",
pages = "296-271",
number = "1",
volume = "39",
doi = "10.1093/imanum/drx067"
}

Milovanović, G. V., Orive, R.,& Spalević, M.. (2019). Quadratures with multiple nodes for Fourier-Chebyshev coefficients. in Ima Journal of Numerical Analysis
Oxford Univ Press, Oxford., 39(1), 271-296.
https://doi.org/10.1093/imanum/drx067

Milovanović GV, Orive R, Spalević M. Quadratures with multiple nodes for Fourier-Chebyshev coefficients. in Ima Journal of Numerical Analysis. 2019;39(1):271-296.
doi:10.1093/imanum/drx067 .

Milovanović, Gradimir V., Orive, Ramon, Spalević, Miodrag, "Quadratures with multiple nodes for Fourier-Chebyshev coefficients" in Ima Journal of Numerical Analysis, 39, no. 1 (2019):271-296,
https://doi.org/10.1093/imanum/drx067 . .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3017
AB  - Generalized averaged Gaussian quadrature rules and truncated variants associated with a nonnegative measure with support on a real open interval {t : a  lt  t  lt  b} may have nodes outside this interval, in other words the rules may fail to be internal. Such rules cannot be applied when the integrand is defined on {t : a  lt  t  lt  b} only. This paper investigates whether generalized averaged Gaussian quadrature rules and truncated variants are internal for measures induced by Chebyshev polynomials. Our results complement those of Notaris [13] for Gauss-Kronrod quadrature formulas for the same kind of measures.
PB  - Elsevier Science Bv, Amsterdam
T2  - Applied Numerical Mathematics
T1  - Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials
EP  - 205
SP  - 190
VL  - 142
DO  - 10.1016/j.apnum.2019.03.008
ER  - 

@article{
author = "Đukić, Dušan and Reichel, Lothar and Spalević, Miodrag",
year = "2019",
abstract = "Generalized averaged Gaussian quadrature rules and truncated variants associated with a nonnegative measure with support on a real open interval {t : a  lt  t  lt  b} may have nodes outside this interval, in other words the rules may fail to be internal. Such rules cannot be applied when the integrand is defined on {t : a  lt  t  lt  b} only. This paper investigates whether generalized averaged Gaussian quadrature rules and truncated variants are internal for measures induced by Chebyshev polynomials. Our results complement those of Notaris [13] for Gauss-Kronrod quadrature formulas for the same kind of measures.",
publisher = "Elsevier Science Bv, Amsterdam",
journal = "Applied Numerical Mathematics",
title = "Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials",
pages = "205-190",
volume = "142",
doi = "10.1016/j.apnum.2019.03.008"
}

Đukić, D., Reichel, L.,& Spalević, M.. (2019). Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials. in Applied Numerical Mathematics
Elsevier Science Bv, Amsterdam., 142, 190-205.
https://doi.org/10.1016/j.apnum.2019.03.008

Đukić D, Reichel L, Spalević M. Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials. in Applied Numerical Mathematics. 2019;142:190-205.
doi:10.1016/j.apnum.2019.03.008 .

Đukić, Dušan, Reichel, Lothar, Spalević, Miodrag, "Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials" in Applied Numerical Mathematics, 142 (2019):190-205,
https://doi.org/10.1016/j.apnum.2019.03.008 . .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
AU  - Tomanović, Jelena
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3078
AB  - Generalized averaged Gaussian quadrature rules associated with some measure, and truncated variants of these rules, can be used to estimate the error in Gaussian quadrature rules. However, the former quadrature rules may have nodes outside the interval of integration and, therefore, it may not be possible to apply them when the integrand is defined on the interval of integration only. This paper investigates whether generalized averaged Gaussian quadrature rules associated with modified Chebyshev measures of the second kind, and truncated variants of these rules, are internal, i.e. if all nodes of these quadrature rules are in the interval of integration.
PB  - Elsevier Science Bv, Amsterdam
T2  - Journal of Computational and Applied Mathematics
T1  - Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind
EP  - 85
SP  - 70
VL  - 345
DO  - 10.1016/j.cam.2018.06.017
ER  - 

@article{
author = "Đukić, Dušan and Reichel, Lothar and Spalević, Miodrag and Tomanović, Jelena",
year = "2019",
abstract = "Generalized averaged Gaussian quadrature rules associated with some measure, and truncated variants of these rules, can be used to estimate the error in Gaussian quadrature rules. However, the former quadrature rules may have nodes outside the interval of integration and, therefore, it may not be possible to apply them when the integrand is defined on the interval of integration only. This paper investigates whether generalized averaged Gaussian quadrature rules associated with modified Chebyshev measures of the second kind, and truncated variants of these rules, are internal, i.e. if all nodes of these quadrature rules are in the interval of integration.",
publisher = "Elsevier Science Bv, Amsterdam",
journal = "Journal of Computational and Applied Mathematics",
title = "Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind",
pages = "85-70",
volume = "345",
doi = "10.1016/j.cam.2018.06.017"
}

Đukić, D., Reichel, L., Spalević, M.,& Tomanović, J.. (2019). Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind. in Journal of Computational and Applied Mathematics
Elsevier Science Bv, Amsterdam., 345, 70-85.
https://doi.org/10.1016/j.cam.2018.06.017

Đukić D, Reichel L, Spalević M, Tomanović J. Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind. in Journal of Computational and Applied Mathematics. 2019;345:70-85.
doi:10.1016/j.cam.2018.06.017 .

Đukić, Dušan, Reichel, Lothar, Spalević, Miodrag, Tomanović, Jelena, "Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind" in Journal of Computational and Applied Mathematics, 345 (2019):70-85,
https://doi.org/10.1016/j.cam.2018.06.017 . .

TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Pranić, Miroslav S.
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3083
AB  - The paper deals with new contributions to the theory of the Gauss quadrature formulas with multiple nodes that are published after 2001, including numerical construction, error analysis and applications. The first part was published in Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials (W. Gautschi, F. Marcellan, and L. Reichel, eds.) [J. Comput. Appl. Math. 127 (2001), no. 1-2, 267-286].
PB  - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
T2  - Applicable Analysis and Discrete Mathematics
T1  - Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii
EP  - 27
IS  - 1
SP  - 1
VL  - 13
DO  - 10.2298/AADM180730018M
ER  - 

@article{
author = "Milovanović, Gradimir V. and Pranić, Miroslav S. and Spalević, Miodrag",
year = "2019",
abstract = "The paper deals with new contributions to the theory of the Gauss quadrature formulas with multiple nodes that are published after 2001, including numerical construction, error analysis and applications. The first part was published in Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials (W. Gautschi, F. Marcellan, and L. Reichel, eds.) [J. Comput. Appl. Math. 127 (2001), no. 1-2, 267-286].",
publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd",
journal = "Applicable Analysis and Discrete Mathematics",
title = "Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii",
pages = "27-1",
number = "1",
volume = "13",
doi = "10.2298/AADM180730018M"
}

Milovanović, G. V., Pranić, M. S.,& Spalević, M.. (2019). Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii. in Applicable Analysis and Discrete Mathematics
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 13(1), 1-27.
https://doi.org/10.2298/AADM180730018M

Milovanović GV, Pranić MS, Spalević M. Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii. in Applicable Analysis and Discrete Mathematics. 2019;13(1):1-27.
doi:10.2298/AADM180730018M .

Milovanović, Gradimir V., Pranić, Miroslav S., Spalević, Miodrag, "Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii" in Applicable Analysis and Discrete Mathematics, 13, no. 1 (2019):1-27,
https://doi.org/10.2298/AADM180730018M . .

TY  - JOUR
AU  - Pejčev, Aleksandar
AU  - Mihić, Ljubica
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3115
AB  - Starting from the explicit expression of the corresponding kernels, derived by Gautschi and Li (W. Gautschi, S. Li: The remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadrature rules with multiple end points, J. Comput. Appl. Math. 33 (1990) 315-329), we determine the exact dimensions of the minimal ellipses on which the modulus of the kernel starts to behave in the described way. The effective error bounds for Gauss-Radau and Gauss-Lobatto quadrature formulas with double end point(s) are derived. The comparisons are made with the actual errors.
PB  - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
T2  - Applicable Analysis and Discrete Mathematics
T1  - Errors of gauss-radau and gauss-lobatto quadratures with double end point
EP  - 477
IS  - 2
SP  - 463
VL  - 13
DO  - 10.2298/AADM180408011P
ER  - 

@article{
author = "Pejčev, Aleksandar and Mihić, Ljubica",
year = "2019",
abstract = "Starting from the explicit expression of the corresponding kernels, derived by Gautschi and Li (W. Gautschi, S. Li: The remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadrature rules with multiple end points, J. Comput. Appl. Math. 33 (1990) 315-329), we determine the exact dimensions of the minimal ellipses on which the modulus of the kernel starts to behave in the described way. The effective error bounds for Gauss-Radau and Gauss-Lobatto quadrature formulas with double end point(s) are derived. The comparisons are made with the actual errors.",
publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd",
journal = "Applicable Analysis and Discrete Mathematics",
title = "Errors of gauss-radau and gauss-lobatto quadratures with double end point",
pages = "477-463",
number = "2",
volume = "13",
doi = "10.2298/AADM180408011P"
}

Pejčev, A.,& Mihić, L.. (2019). Errors of gauss-radau and gauss-lobatto quadratures with double end point. in Applicable Analysis and Discrete Mathematics
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 13(2), 463-477.
https://doi.org/10.2298/AADM180408011P

Pejčev A, Mihić L. Errors of gauss-radau and gauss-lobatto quadratures with double end point. in Applicable Analysis and Discrete Mathematics. 2019;13(2):463-477.
doi:10.2298/AADM180408011P .

Pejčev, Aleksandar, Mihić, Ljubica, "Errors of gauss-radau and gauss-lobatto quadratures with double end point" in Applicable Analysis and Discrete Mathematics, 13, no. 2 (2019):463-477,
https://doi.org/10.2298/AADM180408011P . .

TY  - CONF
AU  - Đukić, Dušan
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6106
AB  - When moments or modi ed moments of the weight function are difficult to
compute, generalized averaged Gaussian quadratures can serve as good substitutes.
These formulas were introduced by Spalević [3], where it was demonstrated
that they may yield a smaller error compared to the Gauss quadrature
rules. However, generalized averaged Gaussian quadratures may have external
nodes. This would make them unusable when the domain of the integrand is
limited to the convex hull of the support of the weight function. In this paper
we investigate whether removing some of the last rows and columns of their
Jacobi matrices (cf. [2]) will produce quadrature rules with no external nodes.
The results that will be presented have been recently published in [1].
PB  - Department of Mathematics, Faculty of Science, Akdeniz University,Turkey
C3  - Proceedings Book of MICOPAM2018 conference
T1  - Internality of truncated averaged Gaussian quadratures
EP  - 66
SP  - 62
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6106
ER  - 

@conference{
author = "Đukić, Dušan and Reichel, Lothar and Spalević, Miodrag",
year = "2018",
abstract = "When moments or modi ed moments of the weight function are difficult to
compute, generalized averaged Gaussian quadratures can serve as good substitutes.
These formulas were introduced by Spalević [3], where it was demonstrated
that they may yield a smaller error compared to the Gauss quadrature
rules. However, generalized averaged Gaussian quadratures may have external
nodes. This would make them unusable when the domain of the integrand is
limited to the convex hull of the support of the weight function. In this paper
we investigate whether removing some of the last rows and columns of their
Jacobi matrices (cf. [2]) will produce quadrature rules with no external nodes.
The results that will be presented have been recently published in [1].",
publisher = "Department of Mathematics, Faculty of Science, Akdeniz University,Turkey",
journal = "Proceedings Book of MICOPAM2018 conference",
title = "Internality of truncated averaged Gaussian quadratures",
pages = "66-62",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6106"
}

Đukić, D., Reichel, L.,& Spalević, M.. (2018). Internality of truncated averaged Gaussian quadratures. in Proceedings Book of MICOPAM2018 conference
Department of Mathematics, Faculty of Science, Akdeniz University,Turkey., 62-66.
https://hdl.handle.net/21.15107/rcub_machinery_6106

Đukić D, Reichel L, Spalević M. Internality of truncated averaged Gaussian quadratures. in Proceedings Book of MICOPAM2018 conference. 2018;:62-66.
https://hdl.handle.net/21.15107/rcub_machinery_6106 .

Đukić, Dušan, Reichel, Lothar, Spalević, Miodrag, "Internality of truncated averaged Gaussian quadratures" in Proceedings Book of MICOPAM2018 conference (2018):62-66,
https://hdl.handle.net/21.15107/rcub_machinery_6106 .

TY  - JOUR
AU  - Mutavdžić Đukić, Rada
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2954
AB  - We consider the Kronrod extension of generalizations of the Micchelli-Rivlin quadrature formula for the Fourier-Chebyshev coefficients with the highest algebraic degree of precision. For analytic functions, the remainder term of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points -/+ 1 and the sum of semi-axes rho > 1 for the mentioned quadrature formulas. We derive L-infinity-error bounds and L-1-error bounds for these quadrature formulas. Finally, we obtain explicit bounds by expanding the remainder term. Numerical examples that compare these error bounds are included.
PB  - Kent State University
T2  - Electronic Transactions on Numerical Analysis
T1  - Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions
EP  - 35
SP  - 20
VL  - 50
DO  - 10.1553/etna-vol50s20
ER  - 

@article{
author = "Mutavdžić Đukić, Rada and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2018",
abstract = "We consider the Kronrod extension of generalizations of the Micchelli-Rivlin quadrature formula for the Fourier-Chebyshev coefficients with the highest algebraic degree of precision. For analytic functions, the remainder term of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points -/+ 1 and the sum of semi-axes rho > 1 for the mentioned quadrature formulas. We derive L-infinity-error bounds and L-1-error bounds for these quadrature formulas. Finally, we obtain explicit bounds by expanding the remainder term. Numerical examples that compare these error bounds are included.",
publisher = "Kent State University",
journal = "Electronic Transactions on Numerical Analysis",
title = "Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions",
pages = "35-20",
volume = "50",
doi = "10.1553/etna-vol50s20"
}

Mutavdžić Đukić, R., Pejčev, A.,& Spalević, M.. (2018). Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions. in Electronic Transactions on Numerical Analysis
Kent State University., 50, 20-35.
https://doi.org/10.1553/etna-vol50s20

Mutavdžić Đukić R, Pejčev A, Spalević M. Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions. in Electronic Transactions on Numerical Analysis. 2018;50:20-35.
doi:10.1553/etna-vol50s20 .

Mutavdžić Đukić, Rada, Pejčev, Aleksandar, Spalević, Miodrag, "Error bounds for kronrod extension of generalizations of micchelli-rivlin quadrature formula for analytic functions" in Electronic Transactions on Numerical Analysis, 50 (2018):20-35,
https://doi.org/10.1553/etna-vol50s20 . .

TY  - JOUR
AU  - Petrović, Andrija
AU  - Svorcan, Jelena
AU  - Pejčev, Aleksandar
AU  - Radenković, Darko
AU  - Petrović, Aleksandar
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2930
AB  - Different applications of a variable area convergent-divergent nozzle are found in various parts of the industry. This paper presents the development of a new design methodology for a variable area convergent-divergent nozzle, to maintain constant nozzle area ratio for different values of mass flow rates. The validation of the presented model was carried out on an example supersonic ejector using experimental, numerical and analytical data. Analytical (one dimensional) and computational fluid dynamics models showed satisfactory prediction performance in comparison with the experiment. The average entrainment ratio error was between 10% and 7%, respectively. Results confirmed that the velocity of the primary fluid at the nozzle outlet is in accordance with the one dimensional analysis. Although disturbances (strong and weak shock waves) are visible, their effects are negligible. Also, supersonic ejector performances are presented through relations between entrainment ratio, outlet pressure and spindle position. Disadvantages of variable area nozzle utilization in ejector applications are emphasized.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematical Modelling
T1  - Comparison of novel variable area convergent-divergent nozzle performances obtained by analytic, computational and experimental methods
EP  - 225
SP  - 206
VL  - 57
DO  - 10.1016/j.apm.2018.01.016
ER  - 

@article{
author = "Petrović, Andrija and Svorcan, Jelena and Pejčev, Aleksandar and Radenković, Darko and Petrović, Aleksandar",
year = "2018",
abstract = "Different applications of a variable area convergent-divergent nozzle are found in various parts of the industry. This paper presents the development of a new design methodology for a variable area convergent-divergent nozzle, to maintain constant nozzle area ratio for different values of mass flow rates. The validation of the presented model was carried out on an example supersonic ejector using experimental, numerical and analytical data. Analytical (one dimensional) and computational fluid dynamics models showed satisfactory prediction performance in comparison with the experiment. The average entrainment ratio error was between 10% and 7%, respectively. Results confirmed that the velocity of the primary fluid at the nozzle outlet is in accordance with the one dimensional analysis. Although disturbances (strong and weak shock waves) are visible, their effects are negligible. Also, supersonic ejector performances are presented through relations between entrainment ratio, outlet pressure and spindle position. Disadvantages of variable area nozzle utilization in ejector applications are emphasized.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematical Modelling",
title = "Comparison of novel variable area convergent-divergent nozzle performances obtained by analytic, computational and experimental methods",
pages = "225-206",
volume = "57",
doi = "10.1016/j.apm.2018.01.016"
}

Petrović, A., Svorcan, J., Pejčev, A., Radenković, D.,& Petrović, A.. (2018). Comparison of novel variable area convergent-divergent nozzle performances obtained by analytic, computational and experimental methods. in Applied Mathematical Modelling
Elsevier Science Inc, New York., 57, 206-225.
https://doi.org/10.1016/j.apm.2018.01.016

Petrović A, Svorcan J, Pejčev A, Radenković D, Petrović A. Comparison of novel variable area convergent-divergent nozzle performances obtained by analytic, computational and experimental methods. in Applied Mathematical Modelling. 2018;57:206-225.
doi:10.1016/j.apm.2018.01.016 .

Petrović, Andrija, Svorcan, Jelena, Pejčev, Aleksandar, Radenković, Darko, Petrović, Aleksandar, "Comparison of novel variable area convergent-divergent nozzle performances obtained by analytic, computational and experimental methods" in Applied Mathematical Modelling, 57 (2018):206-225,
https://doi.org/10.1016/j.apm.2018.01.016 . .

TY  - JOUR
AU  - de la Calle Ysern, B.
AU  - Spalević, Miodrag
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2944
AB  - Modified Stieltjes polynomials are defined and used to construct suboptimal extensions of Gaussian rules with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. We prove that, for wide classes of weight functions and a sufficiently large number of nodes, the extended quadratures have positive weights and simple nodes on the interval . The classes of weight functions considered complement those for which the Gauss-Kronrod rule is known to exist. Also, strong asymptotic representations on the whole interval are given for the modified Stieltjes polynomials, which prove that they behave asymptotically as orthogonal polynomials. Finally, we provide some numerical examples.
PB  - Springer Heidelberg, Heidelberg
T2  - Numerische Mathematik
T1  - Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules
EP  - 35
IS  - 1
SP  - 1
VL  - 138
DO  - 10.1007/s00211-017-0901-y
ER  - 

@article{
author = "de la Calle Ysern, B. and Spalević, Miodrag",
year = "2018",
abstract = "Modified Stieltjes polynomials are defined and used to construct suboptimal extensions of Gaussian rules with one or two degrees less of polynomial exactness than the corresponding Kronrod extension. We prove that, for wide classes of weight functions and a sufficiently large number of nodes, the extended quadratures have positive weights and simple nodes on the interval . The classes of weight functions considered complement those for which the Gauss-Kronrod rule is known to exist. Also, strong asymptotic representations on the whole interval are given for the modified Stieltjes polynomials, which prove that they behave asymptotically as orthogonal polynomials. Finally, we provide some numerical examples.",
publisher = "Springer Heidelberg, Heidelberg",
journal = "Numerische Mathematik",
title = "Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules",
pages = "35-1",
number = "1",
volume = "138",
doi = "10.1007/s00211-017-0901-y"
}

de la Calle Ysern, B.,& Spalević, M.. (2018). Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules. in Numerische Mathematik
Springer Heidelberg, Heidelberg., 138(1), 1-35.
https://doi.org/10.1007/s00211-017-0901-y

de la Calle Ysern B, Spalević M. Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules. in Numerische Mathematik. 2018;138(1):1-35.
doi:10.1007/s00211-017-0901-y .

de la Calle Ysern, B., Spalević, Miodrag, "Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules" in Numerische Mathematik, 138, no. 1 (2018):1-35,
https://doi.org/10.1007/s00211-017-0901-y . .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2933
AB  - We consider the Gauss-Kronrod quadrature formulae for the Bernstein-SzegoIi weight functions consisting of any one of the four Chebyshev weights divided by the polynomial . For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points a" 1 and sum of semi-axes rho > 1, for the given quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed by S. Notaris (Numer. Math. 103, 99-127, 2006).
PB  - Springer, Dordrecht
T2  - Numerical Algorithms
T1  - The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-SzegoIi type
EP  - 1028
IS  - 4
SP  - 1003
VL  - 77
DO  - 10.1007/s11075-017-0351-8
ER  - 

@article{
author = "Đukić, Dušan and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2018",
abstract = "We consider the Gauss-Kronrod quadrature formulae for the Bernstein-SzegoIi weight functions consisting of any one of the four Chebyshev weights divided by the polynomial . For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points a" 1 and sum of semi-axes rho > 1, for the given quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed by S. Notaris (Numer. Math. 103, 99-127, 2006).",
publisher = "Springer, Dordrecht",
journal = "Numerical Algorithms",
title = "The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-SzegoIi type",
pages = "1028-1003",
number = "4",
volume = "77",
doi = "10.1007/s11075-017-0351-8"
}

Đukić, D., Pejčev, A.,& Spalević, M.. (2018). The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-SzegoIi type. in Numerical Algorithms
Springer, Dordrecht., 77(4), 1003-1028.
https://doi.org/10.1007/s11075-017-0351-8

Đukić D, Pejčev A, Spalević M. The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-SzegoIi type. in Numerical Algorithms. 2018;77(4):1003-1028.
doi:10.1007/s11075-017-0351-8 .

Đukić, Dušan, Pejčev, Aleksandar, Spalević, Miodrag, "The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-SzegoIi type" in Numerical Algorithms, 77, no. 4 (2018):1003-1028,
https://doi.org/10.1007/s11075-017-0351-8 . .

TY  - CONF
AU  - Spalević, Miodrag
PY  - 2018
UR  - https://imi.pmf.kg.ac.rs/kongres/pdf/accepted-finished/84ea6b66fe2307dd6fb7926accff42f8_8_04272018_093832/SMAK2018_Spalevic.pdf
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5204
C3  - Тhe 14th Serbian Mathematical Congress (14th SMAK)
T1  - On generalized averaged Gaussian formulas
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5204
ER  - 

@conference{
author = "Spalević, Miodrag",
year = "2018",
journal = "Тhe 14th Serbian Mathematical Congress (14th SMAK)",
title = "On generalized averaged Gaussian formulas",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5204"
}

Spalević, M.. (2018). On generalized averaged Gaussian formulas. in Тhe 14th Serbian Mathematical Congress (14th SMAK).
https://hdl.handle.net/21.15107/rcub_machinery_5204

Spalević M. On generalized averaged Gaussian formulas. in Тhe 14th Serbian Mathematical Congress (14th SMAK). 2018;.
https://hdl.handle.net/21.15107/rcub_machinery_5204 .

Spalević, Miodrag, "On generalized averaged Gaussian formulas" in Тhe 14th Serbian Mathematical Congress (14th SMAK) (2018),
https://hdl.handle.net/21.15107/rcub_machinery_5204 .

TY  - JOUR
AU  - Veljković, Zorica
AU  - Spasojević Brkić, Vesna
AU  - Ćurić, Damir
AU  - Radojević, Slobodan
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2782
AB  - U ovom radu se razmatra upotreba Taguchi-jevog koeficijenta učešća kao i prilagođenog Pareto dijagrama u cilju određivanja veličine uticaja projektovanih faktora u statistički planiranim eksperimentima (tradicionalnim ili Taguchi-jevim) na izlazne veličine u cilju određivanja najbolje kombinacije projektovanih fakora na posmatrane eksperimentalne rezultate u cilju dobijanja optimalnih rešenja. U radu su prikazane dve studije slučaja kod kojih svaki sadrži dva ekstremna rezultata. Prvi primer se odnosi na ispitivanje jednog ulaznog eksperimenta, podeljenog na tri manja u cilju ispitivanja projektovanog realnog, trodimenzionallnog radnog prostora kranista. U ovom primeru kod projektovanog eksperimenta je mereno više izlaznih veličina. Drugi primer se odnosi na dva eksperimenta koja su postavljena na isti način ali sa različitim izlaznim veličinama. Eksperimenti se odnose na geometrijske deformacije dva različita dela razvodnika optičkih kablova koji su različitih dimenzija i izrađuju se od različitih materijala, ali istim procesom livenja plastike, pri čemu je pokazano da eksperimenti imaju različite izlazne veličine, takve da jedan daje rezultate koji su upotrebljivi u praksi, dok su rezultati drugog eksperimenta neupotrebljivi usled velike slučajne greške. Shodno tome rad daje smernice za korišćenje Taguchi-jevog koeficijenta učešća i Pareto dijagrama za efektivno određivanje uticajnih faktora i njihove veličine u oblasti planiranja eksperimenata.
AB  - This paper considers the usage of Taguchi's contribution ratio as well as an adjusted Pareto diagram for determining the size of influential design factors in experimental design on output values in order to determine the best combination of input factors, as well as factors that can determine output. Two case studies that cover extreme examples are presented in that aim. The first case study examines one input workspace design distributed on tree experimental designs defining space coordinates. Every design has several output values that were measured. The second case study presents two experiments regarding injection of plastic molding process, with same input factors at parts which are different in material and dimensions with geometric deformations as output. It was shown that different experiments lead to different results, of which one is acceptable, while other is useless for further examinations. Accordingly, this paper gives guidelines how to use Taguchi's contribution ratio and Pareto diagram effectively in determination of influential factors in experiments.
PB  - Univerzitet u Novom Sadu - Tehnički fakultet Mihajlo Pupin, Zrenjanin
T2  - Journal of Engineering Management and Competitiveness (JEMC)
T1  - Upotreba Taguchi-jevog koeficijenta učešća i Pareto dijagrama u identifikaciji uticajnih faktora u eksperimentima - studije slučajeva
T1  - Using Taguchi's contribution ratio and Pareto diagram in identification of influential factors in experiments: Case studies
EP  - 136
IS  - 2
SP  - 129
VL  - 8
DO  - 10.5937/jemc1802129V
ER  - 

@article{
author = "Veljković, Zorica and Spasojević Brkić, Vesna and Ćurić, Damir and Radojević, Slobodan",
year = "2018",
abstract = "U ovom radu se razmatra upotreba Taguchi-jevog koeficijenta učešća kao i prilagođenog Pareto dijagrama u cilju određivanja veličine uticaja projektovanih faktora u statistički planiranim eksperimentima (tradicionalnim ili Taguchi-jevim) na izlazne veličine u cilju određivanja najbolje kombinacije projektovanih fakora na posmatrane eksperimentalne rezultate u cilju dobijanja optimalnih rešenja. U radu su prikazane dve studije slučaja kod kojih svaki sadrži dva ekstremna rezultata. Prvi primer se odnosi na ispitivanje jednog ulaznog eksperimenta, podeljenog na tri manja u cilju ispitivanja projektovanog realnog, trodimenzionallnog radnog prostora kranista. U ovom primeru kod projektovanog eksperimenta je mereno više izlaznih veličina. Drugi primer se odnosi na dva eksperimenta koja su postavljena na isti način ali sa različitim izlaznim veličinama. Eksperimenti se odnose na geometrijske deformacije dva različita dela razvodnika optičkih kablova koji su različitih dimenzija i izrađuju se od različitih materijala, ali istim procesom livenja plastike, pri čemu je pokazano da eksperimenti imaju različite izlazne veličine, takve da jedan daje rezultate koji su upotrebljivi u praksi, dok su rezultati drugog eksperimenta neupotrebljivi usled velike slučajne greške. Shodno tome rad daje smernice za korišćenje Taguchi-jevog koeficijenta učešća i Pareto dijagrama za efektivno određivanje uticajnih faktora i njihove veličine u oblasti planiranja eksperimenata., This paper considers the usage of Taguchi's contribution ratio as well as an adjusted Pareto diagram for determining the size of influential design factors in experimental design on output values in order to determine the best combination of input factors, as well as factors that can determine output. Two case studies that cover extreme examples are presented in that aim. The first case study examines one input workspace design distributed on tree experimental designs defining space coordinates. Every design has several output values that were measured. The second case study presents two experiments regarding injection of plastic molding process, with same input factors at parts which are different in material and dimensions with geometric deformations as output. It was shown that different experiments lead to different results, of which one is acceptable, while other is useless for further examinations. Accordingly, this paper gives guidelines how to use Taguchi's contribution ratio and Pareto diagram effectively in determination of influential factors in experiments.",
publisher = "Univerzitet u Novom Sadu - Tehnički fakultet Mihajlo Pupin, Zrenjanin",
journal = "Journal of Engineering Management and Competitiveness (JEMC)",
title = "Upotreba Taguchi-jevog koeficijenta učešća i Pareto dijagrama u identifikaciji uticajnih faktora u eksperimentima - studije slučajeva, Using Taguchi's contribution ratio and Pareto diagram in identification of influential factors in experiments: Case studies",
pages = "136-129",
number = "2",
volume = "8",
doi = "10.5937/jemc1802129V"
}

Veljković, Z., Spasojević Brkić, V., Ćurić, D.,& Radojević, S.. (2018). Upotreba Taguchi-jevog koeficijenta učešća i Pareto dijagrama u identifikaciji uticajnih faktora u eksperimentima - studije slučajeva. in Journal of Engineering Management and Competitiveness (JEMC)
Univerzitet u Novom Sadu - Tehnički fakultet Mihajlo Pupin, Zrenjanin., 8(2), 129-136.
https://doi.org/10.5937/jemc1802129V

Veljković Z, Spasojević Brkić V, Ćurić D, Radojević S. Upotreba Taguchi-jevog koeficijenta učešća i Pareto dijagrama u identifikaciji uticajnih faktora u eksperimentima - studije slučajeva. in Journal of Engineering Management and Competitiveness (JEMC). 2018;8(2):129-136.
doi:10.5937/jemc1802129V .

Veljković, Zorica, Spasojević Brkić, Vesna, Ćurić, Damir, Radojević, Slobodan, "Upotreba Taguchi-jevog koeficijenta učešća i Pareto dijagrama u identifikaciji uticajnih faktora u eksperimentima - studije slučajeva" in Journal of Engineering Management and Competitiveness (JEMC), 8, no. 2 (2018):129-136,
https://doi.org/10.5937/jemc1802129V . .

TY  - JOUR
AU  - Mihić, Ljubica
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2798
AB  - S. Li in [Studia Sci. Math. Hungar. 29 (1994) 71-83] proposed a Kronrod type extension to the well-known Turan formula. He showed that such an extension exists for any weight function. For the classical Chebyshev weight function of the first kind, Li found the Kronrod extension of Turan formula that has all its nodes real and belonging to the interval of integration, [-1, 1]. In this paper we show the existence and the uniqueness of the additional two cases - the Kronrod exstensions of corresponding Gauss-Turan quadrature formulas for special case of Gori-Micchelli weight function and for generalized Chebyshev weight function of the second kind, that have all their nodes real and belonging to the integration interval [-1, 1]. Numerical results for the weight coefficients in these cases are presented, while the analytic formulas of the nodes are known.
PB  - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2  - Filomat
T1  - Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions
EP  - 6936
IS  - 20
SP  - 6927
VL  - 32
DO  - 10.2298/FIL1820927M
ER  - 

@article{
author = "Mihić, Ljubica and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2018",
abstract = "S. Li in [Studia Sci. Math. Hungar. 29 (1994) 71-83] proposed a Kronrod type extension to the well-known Turan formula. He showed that such an extension exists for any weight function. For the classical Chebyshev weight function of the first kind, Li found the Kronrod extension of Turan formula that has all its nodes real and belonging to the interval of integration, [-1, 1]. In this paper we show the existence and the uniqueness of the additional two cases - the Kronrod exstensions of corresponding Gauss-Turan quadrature formulas for special case of Gori-Micchelli weight function and for generalized Chebyshev weight function of the second kind, that have all their nodes real and belonging to the integration interval [-1, 1]. Numerical results for the weight coefficients in these cases are presented, while the analytic formulas of the nodes are known.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions",
pages = "6936-6927",
number = "20",
volume = "32",
doi = "10.2298/FIL1820927M"
}

Mihić, L., Pejčev, A.,& Spalević, M.. (2018). Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 32(20), 6927-6936.
https://doi.org/10.2298/FIL1820927M

Mihić L, Pejčev A, Spalević M. Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions. in Filomat. 2018;32(20):6927-6936.
doi:10.2298/FIL1820927M .

Mihić, Ljubica, Pejčev, Aleksandar, Spalević, Miodrag, "Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions" in Filomat, 32, no. 20 (2018):6927-6936,
https://doi.org/10.2298/FIL1820927M . .

TY  - JOUR
AU  - Jandrlić, Davorka
AU  - Spalević, Miodrag
AU  - Tomanović, Jelena
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2822
AB  - We estimate the errors of selected cubature formulae constructed by the product of Gauss quadrature rules. The cases of multiple and (hyper-)surface integrals over n-dimensional cube, simplex, sphere and ball are considered. The error estimates are obtained as the absolute value of the difference between cubature formula constructed by the product of Gauss quadrature rules and cubature formula constructed by the product of corresponding Gauss-Kronrod or corresponding generalized averaged Gaussian quadrature rules. Generalized averaged Gaussian quadrature rule (G) over cap (2l+1) is (2l + 1)-point quadrature formula. It has 2l + 1 nodes and the nodes of the corresponding Gauss rule G(l) with l nodes form a subset, similar to the situation for the (2l + 1)-point Gauss-Kronrod rule H2l+1 associated with G(l). The advantages of (G) over cap (2l+1) are that it exists also when H2l+1 does not, and that the numerical construction of (G) over cap (2l+1), based on recently proposed effective numerical procedure, is simpler than the construction of H2l+1.
PB  - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2  - Filomat
T1  - Error Estimates for Certain Cubature Formulae
EP  - 6902
IS  - 20
SP  - 6893
VL  - 32
DO  - 10.2298/FIL1820893J
ER  - 

@article{
author = "Jandrlić, Davorka and Spalević, Miodrag and Tomanović, Jelena",
year = "2018",
abstract = "We estimate the errors of selected cubature formulae constructed by the product of Gauss quadrature rules. The cases of multiple and (hyper-)surface integrals over n-dimensional cube, simplex, sphere and ball are considered. The error estimates are obtained as the absolute value of the difference between cubature formula constructed by the product of Gauss quadrature rules and cubature formula constructed by the product of corresponding Gauss-Kronrod or corresponding generalized averaged Gaussian quadrature rules. Generalized averaged Gaussian quadrature rule (G) over cap (2l+1) is (2l + 1)-point quadrature formula. It has 2l + 1 nodes and the nodes of the corresponding Gauss rule G(l) with l nodes form a subset, similar to the situation for the (2l + 1)-point Gauss-Kronrod rule H2l+1 associated with G(l). The advantages of (G) over cap (2l+1) are that it exists also when H2l+1 does not, and that the numerical construction of (G) over cap (2l+1), based on recently proposed effective numerical procedure, is simpler than the construction of H2l+1.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "Error Estimates for Certain Cubature Formulae",
pages = "6902-6893",
number = "20",
volume = "32",
doi = "10.2298/FIL1820893J"
}

Jandrlić, D., Spalević, M.,& Tomanović, J.. (2018). Error Estimates for Certain Cubature Formulae. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 32(20), 6893-6902.
https://doi.org/10.2298/FIL1820893J

Jandrlić D, Spalević M, Tomanović J. Error Estimates for Certain Cubature Formulae. in Filomat. 2018;32(20):6893-6902.
doi:10.2298/FIL1820893J .

Jandrlić, Davorka, Spalević, Miodrag, Tomanović, Jelena, "Error Estimates for Certain Cubature Formulae" in Filomat, 32, no. 20 (2018):6893-6902,
https://doi.org/10.2298/FIL1820893J . .

TY  - JOUR
AU  - Pejčev, Aleksandar
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2509
AB  - For analytic functions we study the remainder terms of Gauss quadrature rules with respect to Bernstein-Szego weight functions w(t) = w(alpha,beta,delta)(t) = root 1+t/1-t/beta(beta-2 alpha)t(2) + 2 delta(beta-alpha)t+alpha(2) + delta(2) , t epsilon(-1,1), where 0  lt  alpha  lt  beta, beta not equal 2 alpha, vertical bar delta vertical bar  lt  beta-alpha, and whose denominator is an arbitrary polynomial of exact degree 2 that remains positive on [-1,1]. The subcase alpha = 1, beta = 2/(1 + gamma), -1  lt  gamma  lt  0 and delta = 0 has been considered recently by M. M. Spalevie, Error bounds of Gaussian quadrature formulae for one class of Bernstein-Szego weights, Math. Comp., 82 (2013), 1037-1056.
PB  - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
T2  - Applicable Analysis and Discrete Mathematics
T1  - Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights
EP  - 469
IS  - 2
SP  - 451
VL  - 11
DO  - 10.2298/AADM1702451P
ER  - 

@article{
author = "Pejčev, Aleksandar",
year = "2017",
abstract = "For analytic functions we study the remainder terms of Gauss quadrature rules with respect to Bernstein-Szego weight functions w(t) = w(alpha,beta,delta)(t) = root 1+t/1-t/beta(beta-2 alpha)t(2) + 2 delta(beta-alpha)t+alpha(2) + delta(2) , t epsilon(-1,1), where 0  lt  alpha  lt  beta, beta not equal 2 alpha, vertical bar delta vertical bar  lt  beta-alpha, and whose denominator is an arbitrary polynomial of exact degree 2 that remains positive on [-1,1]. The subcase alpha = 1, beta = 2/(1 + gamma), -1  lt  gamma  lt  0 and delta = 0 has been considered recently by M. M. Spalevie, Error bounds of Gaussian quadrature formulae for one class of Bernstein-Szego weights, Math. Comp., 82 (2013), 1037-1056.",
publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd",
journal = "Applicable Analysis and Discrete Mathematics",
title = "Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights",
pages = "469-451",
number = "2",
volume = "11",
doi = "10.2298/AADM1702451P"
}

Pejčev, A.. (2017). Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights. in Applicable Analysis and Discrete Mathematics
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 11(2), 451-469.
https://doi.org/10.2298/AADM1702451P

Pejčev A. Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights. in Applicable Analysis and Discrete Mathematics. 2017;11(2):451-469.
doi:10.2298/AADM1702451P .

Pejčev, Aleksandar, "Error estimates of gaussian quadrature formulae with the third class of bernstein-szego weights" in Applicable Analysis and Discrete Mathematics, 11, no. 2 (2017):451-469,
https://doi.org/10.2298/AADM1702451P . .

TY  - JOUR
AU  - Eshghi, Nasim
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2731
AB  - Matrix functions of the form f (A) v, where A is a large symmetric matrix, f is a function, and v not equal 0 is a vector, are commonly approximated by first applying a few, say n, steps of the symmetric Lanczos process to A with the initial vector v in order to determine an orthogonal section of A. The latter is represented by a (small) n x n tridiagonal matrix to which f is applied. This approach uses the n first Lanczos vectors provided by the Lanczos process. However, n steps of the Lanczos process yield n + 1 Lanczos vectors. This paper discusses how the (n + 1) st Lanczos vector can be used to improve the quality of the computed approximation of f (A) v. Also the approximation of expressions of the form v(T) f (A) v is considered.
PB  - Kent State University
T2  - Electronic Transactions on Numerical Analysis
T1  - Enhanced matrix function approximation
EP  - 205
SP  - 197
VL  - 47
UR  - https://hdl.handle.net/21.15107/rcub_machinery_2731
ER  - 

@article{
author = "Eshghi, Nasim and Reichel, Lothar and Spalević, Miodrag",
year = "2017",
abstract = "Matrix functions of the form f (A) v, where A is a large symmetric matrix, f is a function, and v not equal 0 is a vector, are commonly approximated by first applying a few, say n, steps of the symmetric Lanczos process to A with the initial vector v in order to determine an orthogonal section of A. The latter is represented by a (small) n x n tridiagonal matrix to which f is applied. This approach uses the n first Lanczos vectors provided by the Lanczos process. However, n steps of the Lanczos process yield n + 1 Lanczos vectors. This paper discusses how the (n + 1) st Lanczos vector can be used to improve the quality of the computed approximation of f (A) v. Also the approximation of expressions of the form v(T) f (A) v is considered.",
publisher = "Kent State University",
journal = "Electronic Transactions on Numerical Analysis",
title = "Enhanced matrix function approximation",
pages = "205-197",
volume = "47",
url = "https://hdl.handle.net/21.15107/rcub_machinery_2731"
}

Eshghi, N., Reichel, L.,& Spalević, M.. (2017). Enhanced matrix function approximation. in Electronic Transactions on Numerical Analysis
Kent State University., 47, 197-205.
https://hdl.handle.net/21.15107/rcub_machinery_2731

Eshghi N, Reichel L, Spalević M. Enhanced matrix function approximation. in Electronic Transactions on Numerical Analysis. 2017;47:197-205.
https://hdl.handle.net/21.15107/rcub_machinery_2731 .

Eshghi, Nasim, Reichel, Lothar, Spalević, Miodrag, "Enhanced matrix function approximation" in Electronic Transactions on Numerical Analysis, 47 (2017):197-205,
https://hdl.handle.net/21.15107/rcub_machinery_2731 .

TY  - JOUR
AU  - Shahzad, Naseer
AU  - Alghamdi, Mohammed Ali
AU  - Alshehri, Sarah
AU  - Aranđelović, Ivan D.
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7743
AB  - A negative answer to an open problem is provided. Fixed point results for α -φ
-contractive mappings in semi-metric spaces are proved. To show the generality of this results, examples are given. Finally, an application of this result to probabilistic spaces is derived.
PB  - International Scientific Research Publications
T2  - Journal of nonlinear science and applications
T1  - Semi-metric spaces and fixed points of  α - φ -contractive maps
EP  - 3156
IS  - 9
SP  - 3147
DO  - ISSN 2008 - 1898
ER  - 

@article{
author = "Shahzad, Naseer and Alghamdi, Mohammed Ali and Alshehri, Sarah and Aranđelović, Ivan D.",
year = "2016",
abstract = "A negative answer to an open problem is provided. Fixed point results for α -φ
-contractive mappings in semi-metric spaces are proved. To show the generality of this results, examples are given. Finally, an application of this result to probabilistic spaces is derived.",
publisher = "International Scientific Research Publications",
journal = "Journal of nonlinear science and applications",
title = "Semi-metric spaces and fixed points of  α - φ -contractive maps",
pages = "3156-3147",
number = "9",
doi = "ISSN 2008 - 1898"
}

Shahzad, N., Alghamdi, M. A., Alshehri, S.,& Aranđelović, I. D.. (2016). Semi-metric spaces and fixed points of  α - φ -contractive maps. in Journal of nonlinear science and applications
International Scientific Research Publications.(9), 3147-3156.
https://doi.org/ISSN 2008 - 1898

Shahzad N, Alghamdi MA, Alshehri S, Aranđelović ID. Semi-metric spaces and fixed points of  α - φ -contractive maps. in Journal of nonlinear science and applications. 2016;(9):3147-3156.
doi:ISSN 2008 - 1898 .

Shahzad, Naseer, Alghamdi, Mohammed Ali, Alshehri, Sarah, Aranđelović, Ivan D., "Semi-metric spaces and fixed points of  α - φ -contractive maps" in Journal of nonlinear science and applications, no. 9 (2016):3147-3156,
https://doi.org/ISSN 2008 - 1898 . .