TY  - JOUR
AU  - Orive, Ramon
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
AU  - Mihić, Ljubica
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/88
AB  - In this paper, we consider the Gauss-Kronrod quadrature formulas for a modified Chebyshev weight. Efficient estimates of the error of these Gauss-Kronrod formulae for analytic functions are obtained, using techniques of contour integration that were introduced by Gautschi and Varga (cf. Gautschi and Varga SIAM J. Numer. Anal. 20, 1170-1186 1983). Some illustrative numerical examples which show both the accuracy of the Gauss-Kronrod formulas and the sharpness of our estimations are displayed. Though for the sake of brevity we restrict ourselves to the first kind Chebyshev weight, a similar analysis may be carried out for the other three Chebyshev type weights; part of the corresponding computations are included in a final appendix.
PB  - Springer, Dordrecht
T2  - Numerical Algorithms
T1  - On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type
DO  - 10.1007/s11075-022-01325-8
ER  - 

@article{
author = "Orive, Ramon and Pejčev, Aleksandar and Spalević, Miodrag and Mihić, Ljubica",
year = "2022",
abstract = "In this paper, we consider the Gauss-Kronrod quadrature formulas for a modified Chebyshev weight. Efficient estimates of the error of these Gauss-Kronrod formulae for analytic functions are obtained, using techniques of contour integration that were introduced by Gautschi and Varga (cf. Gautschi and Varga SIAM J. Numer. Anal. 20, 1170-1186 1983). Some illustrative numerical examples which show both the accuracy of the Gauss-Kronrod formulas and the sharpness of our estimations are displayed. Though for the sake of brevity we restrict ourselves to the first kind Chebyshev weight, a similar analysis may be carried out for the other three Chebyshev type weights; part of the corresponding computations are included in a final appendix.",
publisher = "Springer, Dordrecht",
journal = "Numerical Algorithms",
title = "On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type",
doi = "10.1007/s11075-022-01325-8"
}

Orive, R., Pejčev, A., Spalević, M.,& Mihić, L.. (2022). On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type. in Numerical Algorithms
Springer, Dordrecht..
https://doi.org/10.1007/s11075-022-01325-8

Orive R, Pejčev A, Spalević M, Mihić L. On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type. in Numerical Algorithms. 2022;.
doi:10.1007/s11075-022-01325-8 .

Orive, Ramon, Pejčev, Aleksandar, Spalević, Miodrag, Mihić, Ljubica, "On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type" in Numerical Algorithms (2022),
https://doi.org/10.1007/s11075-022-01325-8 . .

TY  - CONF
AU  - Orive, Ramon
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5160
PB  - Faculty of Mechanical Engineering, University of Belgrade
C3  - NMLSP conference, Book of abstracts
T1  - The error bounds of Gauss quadrature formula for the modified weight functions of Chebyshev type
T1  - The error bounds of Gauss quadrature formula for the modified weight functions of Chebyshev type
EP  - 66
SP  - 66
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5160
ER  - 

@conference{
author = "Orive, Ramon and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2022",
publisher = "Faculty of Mechanical Engineering, University of Belgrade",
journal = "NMLSP conference, Book of abstracts",
title = "The error bounds of Gauss quadrature formula for the modified weight functions of Chebyshev type, The error bounds of Gauss quadrature formula for the modified weight functions of Chebyshev type",
pages = "66-66",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5160"
}

Orive, R., Pejčev, A.,& Spalević, M.. (2022). The error bounds of Gauss quadrature formula for the modified weight functions of Chebyshev type. in NMLSP conference, Book of abstracts
Faculty of Mechanical Engineering, University of Belgrade., 66-66.
https://hdl.handle.net/21.15107/rcub_machinery_5160

Orive R, Pejčev A, Spalević M. The error bounds of Gauss quadrature formula for the modified weight functions of Chebyshev type. in NMLSP conference, Book of abstracts. 2022;:66-66.
https://hdl.handle.net/21.15107/rcub_machinery_5160 .

Orive, Ramon, Pejčev, Aleksandar, Spalević, Miodrag, "The error bounds of Gauss quadrature formula for the modified weight functions of Chebyshev type" in NMLSP conference, Book of abstracts (2022):66-66,
https://hdl.handle.net/21.15107/rcub_machinery_5160 .

TY  - CHAP
AU  - Mihić, Ljubica
AU  - Orive, Ramon
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5163
PB  - Faculty of Mechanical Engineering, University of Belgrade
T2  - MNA conference, Book of abstracts
T1  - On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type
EP  - 21
SP  - 21
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5163
ER  - 

@inbook{
author = "Mihić, Ljubica and Orive, Ramon and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2022",
publisher = "Faculty of Mechanical Engineering, University of Belgrade",
journal = "MNA conference, Book of abstracts",
booktitle = "On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type",
pages = "21-21",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5163"
}

Mihić, L., Orive, R., Pejčev, A.,& Spalević, M.. (2022). On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type. in MNA conference, Book of abstracts
Faculty of Mechanical Engineering, University of Belgrade., 21-21.
https://hdl.handle.net/21.15107/rcub_machinery_5163

Mihić L, Orive R, Pejčev A, Spalević M. On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type. in MNA conference, Book of abstracts. 2022;:21-21.
https://hdl.handle.net/21.15107/rcub_machinery_5163 .

Mihić, Ljubica, Orive, Ramon, Pejčev, Aleksandar, Spalević, Miodrag, "On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type" in MNA conference, Book of abstracts (2022):21-21,
https://hdl.handle.net/21.15107/rcub_machinery_5163 .

TY  - JOUR
AU  - Orive, Ramon
AU  - Santos-Leon, Juan C.
AU  - Spalević, Miodrag
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3282
AB  - In this paper we review some of the main known facts about cubature rules to approximate integrals over domains in R-n, in particular with respect to the Gaussian weight w(x) = e(-xTx); where x = (x(1); ... ; x(n)) is an element of R-n. Some new rules are also presented. Taking into account the well-known issue of the "curse of dimensionality", our aim is at providing rules with a certain degree of algebraic precision and a reasonably small number of nodes as well as an acceptable stability. We think that the methods used to construct these new rules are of further applicability in the field of cubature formulas. The efficiency of new and old rules are compared by means of several numerical experiments.
PB  - Kent State University, Kent
T2  - Electronic Transactions on Numerical Analysis
T1  - Cubature formulae for the gaussian weight. Some old and new rules.
EP  - 438
SP  - 426
VL  - 53
DO  - 10.1553/etna_vol53s426
ER  - 

@article{
author = "Orive, Ramon and Santos-Leon, Juan C. and Spalević, Miodrag",
year = "2020",
abstract = "In this paper we review some of the main known facts about cubature rules to approximate integrals over domains in R-n, in particular with respect to the Gaussian weight w(x) = e(-xTx); where x = (x(1); ... ; x(n)) is an element of R-n. Some new rules are also presented. Taking into account the well-known issue of the "curse of dimensionality", our aim is at providing rules with a certain degree of algebraic precision and a reasonably small number of nodes as well as an acceptable stability. We think that the methods used to construct these new rules are of further applicability in the field of cubature formulas. The efficiency of new and old rules are compared by means of several numerical experiments.",
publisher = "Kent State University, Kent",
journal = "Electronic Transactions on Numerical Analysis",
title = "Cubature formulae for the gaussian weight. Some old and new rules.",
pages = "438-426",
volume = "53",
doi = "10.1553/etna_vol53s426"
}

Orive, R., Santos-Leon, J. C.,& Spalević, M.. (2020). Cubature formulae for the gaussian weight. Some old and new rules.. in Electronic Transactions on Numerical Analysis
Kent State University, Kent., 53, 426-438.
https://doi.org/10.1553/etna_vol53s426

Orive R, Santos-Leon JC, Spalević M. Cubature formulae for the gaussian weight. Some old and new rules.. in Electronic Transactions on Numerical Analysis. 2020;53:426-438.
doi:10.1553/etna_vol53s426 .

Orive, Ramon, Santos-Leon, Juan C., Spalević, Miodrag, "Cubature formulae for the gaussian weight. Some old and new rules." in Electronic Transactions on Numerical Analysis, 53 (2020):426-438,
https://doi.org/10.1553/etna_vol53s426 . .

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  - 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  - CONF
AU  - Orive, Ramon
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5339
AB  - In this paper, Gaussian rules for some modi ed Chebyshev weights introduced
by Gautschi and Li in 1993 are considered. Our main concern is providing
efficient estimations for the error of quadrature. Those estimations are checked
by means of some numerical examples.
PB  - Department of Mathematics, Faculty of Science, Akdeniz University,Turkey
C3  - Proceedings Book of MICOPAM2018 conference
T1  - On Gaussian rules for some modi ed Chebyshev weights
EP  - 61
SP  - 58
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5339
ER  - 

@conference{
author = "Orive, Ramon and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2018",
abstract = "In this paper, Gaussian rules for some modi ed Chebyshev weights introduced
by Gautschi and Li in 1993 are considered. Our main concern is providing
efficient estimations for the error of quadrature. Those estimations are checked
by means of some numerical examples.",
publisher = "Department of Mathematics, Faculty of Science, Akdeniz University,Turkey",
journal = "Proceedings Book of MICOPAM2018 conference",
title = "On Gaussian rules for some modi ed Chebyshev weights",
pages = "61-58",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5339"
}

Orive, R., Pejčev, A.,& Spalević, M.. (2018). On Gaussian rules for some modi ed Chebyshev weights. in Proceedings Book of MICOPAM2018 conference
Department of Mathematics, Faculty of Science, Akdeniz University,Turkey., 58-61.
https://hdl.handle.net/21.15107/rcub_machinery_5339

Orive R, Pejčev A, Spalević M. On Gaussian rules for some modi ed Chebyshev weights. in Proceedings Book of MICOPAM2018 conference. 2018;:58-61.
https://hdl.handle.net/21.15107/rcub_machinery_5339 .

Orive, Ramon, Pejčev, Aleksandar, Spalević, Miodrag, "On Gaussian rules for some modi ed Chebyshev weights" in Proceedings Book of MICOPAM2018 conference (2018):58-61,
https://hdl.handle.net/21.15107/rcub_machinery_5339 .

TY  - CONF
AU  - Milovanović, Gradimir
AU  - Orive, Ramon
AU  - Spalević, Miodrag
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5137
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 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. 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 estimation
their error. Numerical results are included. These results are continuation of the
recent ones by Bojanov and Petrova (J. Comput. Appl. Math., 2009), and Milovanovi´c and Spalevi´c (Math. Comp., 2014).
PB  - UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA
C3  - 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA,  BOOK OF ABSTRACTS
T1  - QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS
EP  - 25
SP  - 25
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5137
ER  - 

@conference{
author = "Milovanović, Gradimir and Orive, Ramon and Spalević, Miodrag",
year = "2016",
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 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. 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 estimation
their error. Numerical results are included. These results are continuation of the
recent ones by Bojanov and Petrova (J. Comput. Appl. Math., 2009), and Milovanovi´c and Spalevi´c (Math. Comp., 2014).",
publisher = "UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA",
journal = "6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA,  BOOK OF ABSTRACTS",
title = "QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS",
pages = "25-25",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5137"
}

Milovanović, G., Orive, R.,& Spalević, M.. (2016). QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS. in 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA,  BOOK OF ABSTRACTS
UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA., 25-25.
https://hdl.handle.net/21.15107/rcub_machinery_5137

Milovanović G, Orive R, Spalević M. QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS. in 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA,  BOOK OF ABSTRACTS. 2016;:25-25.
https://hdl.handle.net/21.15107/rcub_machinery_5137 .

Milovanović, Gradimir, Orive, Ramon, Spalević, Miodrag, "QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS" in 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA,  BOOK OF ABSTRACTS (2016):25-25,
https://hdl.handle.net/21.15107/rcub_machinery_5137 .