TY  - JOUR
AU  - Fermo, Luisa
AU  - Reichel, Lothar
AU  - Rodriguez, Giuseppe
AU  - Spalević, Miodrag
PY  - 2024
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7357
PB  - Elsevier
T2  - Applied Mathematics and Computation
T1  - Averaged Nystr\" om  interpolants for the solution of Fredholm integral equations of the second kind
DO  - 10.1016/j.amc.2023.128482
ER  - 

@article{
author = "Fermo, Luisa and Reichel, Lothar and Rodriguez, Giuseppe and Spalević, Miodrag",
year = "2024",
publisher = "Elsevier",
journal = "Applied Mathematics and Computation",
title = "Averaged Nystr\" om  interpolants for the solution of Fredholm integral equations of the second kind",
doi = "10.1016/j.amc.2023.128482"
}

Fermo, L., Reichel, L., Rodriguez, G.,& Spalević, M.. (2024). Averaged Nystr\" om  interpolants for the solution of Fredholm integral equations of the second kind. in Applied Mathematics and Computation
Elsevier..
https://doi.org/10.1016/j.amc.2023.128482

Fermo L, Reichel L, Rodriguez G, Spalević M. Averaged Nystr\" om  interpolants for the solution of Fredholm integral equations of the second kind. in Applied Mathematics and Computation. 2024;.
doi:10.1016/j.amc.2023.128482 .

Fermo, Luisa, Reichel, Lothar, Rodriguez, Giuseppe, Spalević, Miodrag, "Averaged Nystr\" om  interpolants for the solution of Fredholm integral equations of the second kind" in Applied Mathematics and Computation (2024),
https://doi.org/10.1016/j.amc.2023.128482 . .

TY  - JOUR
AU  - Jandrlić, Davorka
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2024
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7069
AB  - In this paper we present an extension of our previous research, focusing on a method to numerically evaluate the error term in the Gaussian quadrature formula with the Legendre weight function, as discussed by Jandrlic et al. (2022). For an analytic integrand, the error term in Gaussian quadrature can be expressed as a contour integral. Consequently, determining the upper bound of the error term involves identifying the maximum value of the modulus of the kernel within the subintegral expression for the error along this contour. In our previous study, we investigated the position of this maximum point on the ellipse for Legendre polynomials. In this paper, we establish sufficient conditions for the maximum of the modulus of the kernel, which we derived analytically, to occur at one of the semi-axes for Gegenbauer polynomials. This result extends to a significantly broader case. We present an effective error estimation that we compare with the actual one. Some numerical results are presented.
PB  - Elsevier
T2  - Journal of Computational and Applied Mathematics
T1  - Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions
IS  - Art.  115586
VL  - 440
DO  - 10.1016/j.cam.2023.115661
ER  - 

@article{
author = "Jandrlić, Davorka and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2024",
abstract = "In this paper we present an extension of our previous research, focusing on a method to numerically evaluate the error term in the Gaussian quadrature formula with the Legendre weight function, as discussed by Jandrlic et al. (2022). For an analytic integrand, the error term in Gaussian quadrature can be expressed as a contour integral. Consequently, determining the upper bound of the error term involves identifying the maximum value of the modulus of the kernel within the subintegral expression for the error along this contour. In our previous study, we investigated the position of this maximum point on the ellipse for Legendre polynomials. In this paper, we establish sufficient conditions for the maximum of the modulus of the kernel, which we derived analytically, to occur at one of the semi-axes for Gegenbauer polynomials. This result extends to a significantly broader case. We present an effective error estimation that we compare with the actual one. Some numerical results are presented.",
publisher = "Elsevier",
journal = "Journal of Computational and Applied Mathematics",
title = "Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions",
number = "Art.  115586",
volume = "440",
doi = "10.1016/j.cam.2023.115661"
}

Jandrlić, D., Pejčev, A.,& Spalević, M.. (2024). Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions. in Journal of Computational and Applied Mathematics
Elsevier., 440(Art.  115586).
https://doi.org/10.1016/j.cam.2023.115661

Jandrlić D, Pejčev A, Spalević M. Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions. in Journal of Computational and Applied Mathematics. 2024;440(Art.  115586).
doi:10.1016/j.cam.2023.115661 .

Jandrlić, Davorka, Pejčev, Aleksandar, Spalević, Miodrag, "Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions" in Journal of Computational and Applied Mathematics, 440, no. Art.  115586 (2024),
https://doi.org/10.1016/j.cam.2023.115661 . .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2024
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7068
AB  - Optimal averaged Gauss quadrature rules provide estimates for the quadrature error in Gauss rules, as well as estimates for the error incurred when approximating
matrix functionals of the form u
T
f (A)v with a large matrix A ∈ R
N×N by lowrank approximations that are obtained by applying a few steps of the symmetric or
nonsymmetric Lanczos processes to A; here u, v ∈ R
N
are vectors. The latter process
is used when the measure associated with the Gauss quadrature rule has support in
the complex plane. The symmetric Lanczos process yields a real tridiagonal matrix,
whose entries determine the recursion coefficients of the monic orthogonal polynomials
associated with the measure, while the nonsymmetric Lanczos process determines a
nonsymmetric tridiagonal matrix, whose entries are recursion coefficients for a pair of
sets of bi-orthogonal polynomials. Recently, it has been shown, by applying the results
of Peherstorfer, that optimal averaged Gauss quadrature rules, which are associated
with a nonnegative measure with support on the real axis, can be expressed as a
weighted sum of two quadrature rules. This decomposition allows faster evaluation of
optimal averaged Gauss quadrature rules than the previously available representation.
The present paper provides a new self-contained proof of this decomposition that
is based on linear algebra techniques. Moreover, these techniques are generalized to
determine a decomposition of the optimal averaged quadrature rules that are associated
with the tridiagonal matrices determined by the nonsymmetric Lanczos process. Also,
the splitting of complex symmetric tridiagonal matrices is discussed. The new splittings
allow faster evaluation of optimal averaged Gauss quadrature rules than the previously
available representations. Computational aspects are discussed.
PB  - Elsevier
T2  - Journal of Computational and Applied Mathematics
T1  - Decompositions of optimal averaged Gauss quadrature rules
IS  - Art.  115586
VL  - 438
DO  - 10.1016/j.cam.2023.115586
ER  - 

@article{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2024",
abstract = "Optimal averaged Gauss quadrature rules provide estimates for the quadrature error in Gauss rules, as well as estimates for the error incurred when approximating
matrix functionals of the form u
T
f (A)v with a large matrix A ∈ R
N×N by lowrank approximations that are obtained by applying a few steps of the symmetric or
nonsymmetric Lanczos processes to A; here u, v ∈ R
N
are vectors. The latter process
is used when the measure associated with the Gauss quadrature rule has support in
the complex plane. The symmetric Lanczos process yields a real tridiagonal matrix,
whose entries determine the recursion coefficients of the monic orthogonal polynomials
associated with the measure, while the nonsymmetric Lanczos process determines a
nonsymmetric tridiagonal matrix, whose entries are recursion coefficients for a pair of
sets of bi-orthogonal polynomials. Recently, it has been shown, by applying the results
of Peherstorfer, that optimal averaged Gauss quadrature rules, which are associated
with a nonnegative measure with support on the real axis, can be expressed as a
weighted sum of two quadrature rules. This decomposition allows faster evaluation of
optimal averaged Gauss quadrature rules than the previously available representation.
The present paper provides a new self-contained proof of this decomposition that
is based on linear algebra techniques. Moreover, these techniques are generalized to
determine a decomposition of the optimal averaged quadrature rules that are associated
with the tridiagonal matrices determined by the nonsymmetric Lanczos process. Also,
the splitting of complex symmetric tridiagonal matrices is discussed. The new splittings
allow faster evaluation of optimal averaged Gauss quadrature rules than the previously
available representations. Computational aspects are discussed.",
publisher = "Elsevier",
journal = "Journal of Computational and Applied Mathematics",
title = "Decompositions of optimal averaged Gauss quadrature rules",
number = "Art.  115586",
volume = "438",
doi = "10.1016/j.cam.2023.115586"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2024). Decompositions of optimal averaged Gauss quadrature rules. in Journal of Computational and Applied Mathematics
Elsevier., 438(Art.  115586).
https://doi.org/10.1016/j.cam.2023.115586

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Decompositions of optimal averaged Gauss quadrature rules. in Journal of Computational and Applied Mathematics. 2024;438(Art.  115586).
doi:10.1016/j.cam.2023.115586 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Decompositions of optimal averaged Gauss quadrature rules" in Journal of Computational and Applied Mathematics, 438, no. Art.  115586 (2024),
https://doi.org/10.1016/j.cam.2023.115586 . .

TY  - JOUR
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2024
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7067
AB  - We describe numerical methods for the construction of interpolatory quadrature rules of Radau and Lobatto types. In particular, we are interested in deriving efficient algorithms for computing optimal averaged Gauss–Radau and Gauss–Lobatto type javascript:undefined;quadrature rules. These averaged rules allow us to estimate the quadrature error in Gauss–Radau and Gauss–Lobatto quadrature rules. This is important since the latter rules have higher algebraic degree of exactness than the corresponding Gauss rules, and this makes it possible to construct averaged quadrature rules of higher algebraic degree of exactness than the corresponding “standard” averaged Gauss rules available in the literature.
PB  - Elsevier
T2  - Journal of Computational and Applied Mathematics
T1  - Radau-  and Lobatto-type averaged Gauss rules
IS  - Art  115477
VL  - 437
DO  - 10.1016/j.cam.2023.115475
ER  - 

@article{
author = "Reichel, Lothar and Spalević, Miodrag",
year = "2024",
abstract = "We describe numerical methods for the construction of interpolatory quadrature rules of Radau and Lobatto types. In particular, we are interested in deriving efficient algorithms for computing optimal averaged Gauss–Radau and Gauss–Lobatto type javascript:undefined;quadrature rules. These averaged rules allow us to estimate the quadrature error in Gauss–Radau and Gauss–Lobatto quadrature rules. This is important since the latter rules have higher algebraic degree of exactness than the corresponding Gauss rules, and this makes it possible to construct averaged quadrature rules of higher algebraic degree of exactness than the corresponding “standard” averaged Gauss rules available in the literature.",
publisher = "Elsevier",
journal = "Journal of Computational and Applied Mathematics",
title = "Radau-  and Lobatto-type averaged Gauss rules",
number = "Art  115477",
volume = "437",
doi = "10.1016/j.cam.2023.115475"
}

Reichel, L.,& Spalević, M.. (2024). Radau-  and Lobatto-type averaged Gauss rules. in Journal of Computational and Applied Mathematics
Elsevier., 437(Art  115477).
https://doi.org/10.1016/j.cam.2023.115475

Reichel L, Spalević M. Radau-  and Lobatto-type averaged Gauss rules. in Journal of Computational and Applied Mathematics. 2024;437(Art  115477).
doi:10.1016/j.cam.2023.115475 .

Reichel, Lothar, Spalević, Miodrag, "Radau-  and Lobatto-type averaged Gauss rules" in Journal of Computational and Applied Mathematics, 437, no. Art  115477 (2024),
https://doi.org/10.1016/j.cam.2023.115475 . .

TY  - CONF
AU  - Spalević, Miodrag
PY  - 2023
UR  - https://icoles.net/wp-content/uploads/abstractsproceedings/abstract2023.pdf
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7664
AB  - We describe numerical methods for the construction of interpolatory quadrature rules of Radau and Lobatto types. In particular, we are interested in deriving efficient algorithms for computing optimal averaged Gauss-Radau and Gauss-Lobatto type quadrature rules. These averaged rules allow us to estimate the quadrature error in Gauss-Radau and Gauss-Lobatto quadrature rules. This is important since the latter rules have higher algebraic degree of exactness than the corresponding Gauss rules, and this makes it possible to construct averaged quadrature rules of higher algebraic degree of exactness than the corresponding “stan- dard'' averaged Gauss rules available in the literature. This is the joint research with Lothar Reichel (Kent State University, U.S.)
C3  - Abstract Book of the ICOLES 2023, 6th INTERNATIONAL CONFERENCE  ON LIFE AND ENGINEERING SCIENCES  ANTALYA, TURKEY NOVEMBER 2-5, 2023
T1  - Radau- and Lobatto-Type Averaged Gauss Rules
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7664
ER  - 

@conference{
author = "Spalević, Miodrag",
year = "2023",
abstract = "We describe numerical methods for the construction of interpolatory quadrature rules of Radau and Lobatto types. In particular, we are interested in deriving efficient algorithms for computing optimal averaged Gauss-Radau and Gauss-Lobatto type quadrature rules. These averaged rules allow us to estimate the quadrature error in Gauss-Radau and Gauss-Lobatto quadrature rules. This is important since the latter rules have higher algebraic degree of exactness than the corresponding Gauss rules, and this makes it possible to construct averaged quadrature rules of higher algebraic degree of exactness than the corresponding “stan- dard'' averaged Gauss rules available in the literature. This is the joint research with Lothar Reichel (Kent State University, U.S.)",
journal = "Abstract Book of the ICOLES 2023, 6th INTERNATIONAL CONFERENCE  ON LIFE AND ENGINEERING SCIENCES  ANTALYA, TURKEY NOVEMBER 2-5, 2023",
title = "Radau- and Lobatto-Type Averaged Gauss Rules",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7664"
}

Spalević, M.. (2023). Radau- and Lobatto-Type Averaged Gauss Rules. in Abstract Book of the ICOLES 2023, 6th INTERNATIONAL CONFERENCE  ON LIFE AND ENGINEERING SCIENCES  ANTALYA, TURKEY NOVEMBER 2-5, 2023.
https://hdl.handle.net/21.15107/rcub_machinery_7664

Spalević M. Radau- and Lobatto-Type Averaged Gauss Rules. in Abstract Book of the ICOLES 2023, 6th INTERNATIONAL CONFERENCE  ON LIFE AND ENGINEERING SCIENCES  ANTALYA, TURKEY NOVEMBER 2-5, 2023. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7664 .

Spalević, Miodrag, "Radau- and Lobatto-Type Averaged Gauss Rules" in Abstract Book of the ICOLES 2023, 6th INTERNATIONAL CONFERENCE  ON LIFE AND ENGINEERING SCIENCES  ANTALYA, TURKEY NOVEMBER 2-5, 2023 (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7664 .

TY  - CONF
AU  - Jandrlić, Davorka
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2023
UR  - http://www.ic-mrs.org/
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7663
C3  - 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS
T1  - Error Estimates for Gaussian Quadrature of Analytic Functions
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7663
ER  - 

@conference{
author = "Jandrlić, Davorka and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2023",
journal = "6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS",
title = "Error Estimates for Gaussian Quadrature of Analytic Functions",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7663"
}

Jandrlić, D., Pejčev, A.,& Spalević, M.. (2023). Error Estimates for Gaussian Quadrature of Analytic Functions. in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS.
https://hdl.handle.net/21.15107/rcub_machinery_7663

Jandrlić D, Pejčev A, Spalević M. Error Estimates for Gaussian Quadrature of Analytic Functions. in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7663 .

Jandrlić, Davorka, Pejčev, Aleksandar, Spalević, Miodrag, "Error Estimates for Gaussian Quadrature of Analytic Functions" in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7663 .

TY  - CONF
AU  - Spalević, Miodrag
PY  - 2023
UR  - http://www.ic-mrs.org/  chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/http://www.ic-mrs.org/files/abstracts-2023.pdf
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7661
AB  - Gauss-Kronrod quadrature rules (named the quadratures of the 20th century) have been developing in the last 60 years in order to solve the question of efficient estimating the error of the Gauss quadrature formula. Anti-Gauss and the generalized averaged Gaussian quadrature rules, as well as their Radau and Lobatto extensions, are introduced lately as alternatives to the Gauss-Kronrod. We present here a survey of the results on their stable numerical calculation.
C3  - 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS
T1  - Numerical Computation of Generalized Averaged Gaussian and AntiGauss Quadrature Rules
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7661
ER  - 

@conference{
author = "Spalević, Miodrag",
year = "2023",
abstract = "Gauss-Kronrod quadrature rules (named the quadratures of the 20th century) have been developing in the last 60 years in order to solve the question of efficient estimating the error of the Gauss quadrature formula. Anti-Gauss and the generalized averaged Gaussian quadrature rules, as well as their Radau and Lobatto extensions, are introduced lately as alternatives to the Gauss-Kronrod. We present here a survey of the results on their stable numerical calculation.",
journal = "6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS",
title = "Numerical Computation of Generalized Averaged Gaussian and AntiGauss Quadrature Rules",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7661"
}

Spalević, M.. (2023). Numerical Computation of Generalized Averaged Gaussian and AntiGauss Quadrature Rules. in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS.
https://hdl.handle.net/21.15107/rcub_machinery_7661

Spalević M. Numerical Computation of Generalized Averaged Gaussian and AntiGauss Quadrature Rules. in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7661 .

Spalević, Miodrag, "Numerical Computation of Generalized Averaged Gaussian and AntiGauss Quadrature Rules" in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7661 .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7065
AB  - Pad\'{e}-type approximants are rational functions that approximate a given formal power series. Boutry \cite{Bo} constructed Pad\'{e}-type approximants that correspond to the averaged Gauss quadrature rules introduced by Laurie \cite{La}. More recently, Spalevi\'c \cite{Sp1} proposed optimal averaged Gauss quadrature rules, that have higher degree of precision than the corresponding averaged Gauss rule, with the same number of nodes. This paper defines Pad\'e-type approximants associated with optimal averaged Gauss rules. Numerical examples illustrate their performance.
PB  - the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM)
T2  - ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
T1  - Optimal Averaged Pade-Type Approximants
EP  - 156
SP  - 145
VL  - 59
DO  - 10.1553/etna_vol59s145
ER  - 

@article{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2023",
abstract = "Pad\'{e}-type approximants are rational functions that approximate a given formal power series. Boutry \cite{Bo} constructed Pad\'{e}-type approximants that correspond to the averaged Gauss quadrature rules introduced by Laurie \cite{La}. More recently, Spalevi\'c \cite{Sp1} proposed optimal averaged Gauss quadrature rules, that have higher degree of precision than the corresponding averaged Gauss rule, with the same number of nodes. This paper defines Pad\'e-type approximants associated with optimal averaged Gauss rules. Numerical examples illustrate their performance.",
publisher = "the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM)",
journal = "ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS",
title = "Optimal Averaged Pade-Type Approximants",
pages = "156-145",
volume = "59",
doi = "10.1553/etna_vol59s145"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2023). Optimal Averaged Pade-Type Approximants. in ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM)., 59, 145-156.
https://doi.org/10.1553/etna_vol59s145

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Optimal Averaged Pade-Type Approximants. in ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. 2023;59:145-156.
doi:10.1553/etna_vol59s145 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Optimal Averaged Pade-Type Approximants" in ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 59 (2023):145-156,
https://doi.org/10.1553/etna_vol59s145 . .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7066
AB  - This paper is concerned with the approximation of integrals of a real-valued integrand over
the interval [−1, 1] by Gauss quadrature. The averaged and optimal averaged quadrature
rules ([13,21]) provide a convenient method for approximating the error in the Gauss
quadrature. However, they are applicable to all integrands that are continuous on the
interval [−1, 1] only if their nodes are internal, i.e. if they belong to this interval.
We discuss two approaches to determine averaged quadrature rules with nodes in
[−1, 1]: (i) truncating the Jacobi matrix associated with the optimal averaged rule, and
(ii) weighting the optimal averaged quadrature rule. We consider Chebyshev measures of
the first, second, and third kinds that are modified by a linear over linear rational factor,
and discuss the internality of averaged, optimal averaged, and truncated optimal averaged
quadrature rules. Moreover, we show that the weighting yields internal averaged rules
if a weighting parameter is properly chosen, and we provide bounds for this parameter
that guarantee internality. Finally, we illustrate that the weighted averaged rules give more
accurate estimates of the quadrature error than the truncated optimal averaged rules.
PB  - Elsevier
T2  - Applied Numerical Mathematics
T1  - Weighted averaged Gaussian quadrature rules for modified Chebyshev measures
DO  - 10.1016/j.apnum.2023.05.014
ER  - 

@article{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2023",
abstract = "This paper is concerned with the approximation of integrals of a real-valued integrand over
the interval [−1, 1] by Gauss quadrature. The averaged and optimal averaged quadrature
rules ([13,21]) provide a convenient method for approximating the error in the Gauss
quadrature. However, they are applicable to all integrands that are continuous on the
interval [−1, 1] only if their nodes are internal, i.e. if they belong to this interval.
We discuss two approaches to determine averaged quadrature rules with nodes in
[−1, 1]: (i) truncating the Jacobi matrix associated with the optimal averaged rule, and
(ii) weighting the optimal averaged quadrature rule. We consider Chebyshev measures of
the first, second, and third kinds that are modified by a linear over linear rational factor,
and discuss the internality of averaged, optimal averaged, and truncated optimal averaged
quadrature rules. Moreover, we show that the weighting yields internal averaged rules
if a weighting parameter is properly chosen, and we provide bounds for this parameter
that guarantee internality. Finally, we illustrate that the weighted averaged rules give more
accurate estimates of the quadrature error than the truncated optimal averaged rules.",
publisher = "Elsevier",
journal = "Applied Numerical Mathematics",
title = "Weighted averaged Gaussian quadrature rules for modified Chebyshev measures",
doi = "10.1016/j.apnum.2023.05.014"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2023). Weighted averaged Gaussian quadrature rules for modified Chebyshev measures. in Applied Numerical Mathematics
Elsevier..
https://doi.org/10.1016/j.apnum.2023.05.014

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Weighted averaged Gaussian quadrature rules for modified Chebyshev measures. in Applied Numerical Mathematics. 2023;.
doi:10.1016/j.apnum.2023.05.014 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Weighted averaged Gaussian quadrature rules for modified Chebyshev measures" in Applied Numerical Mathematics (2023),
https://doi.org/10.1016/j.apnum.2023.05.014 . .

TY  - CONF
AU  - Spalević, Miodrag
PY  - 2023
UR  - http://www.ic-mrs.org/files/program-2023.pdf
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7217
C3  - 6th International Conference on Mathematics and Related Sciences (ICMRS 2023), online meeting,  Turkey
T1  - Numerical  Computation of Generalized  Averaged  Gaussian  and  Anti-Gauss  Quadrature  Rules
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7217
ER  - 

@conference{
author = "Spalević, Miodrag",
year = "2023",
journal = "6th International Conference on Mathematics and Related Sciences (ICMRS 2023), online meeting,  Turkey",
title = "Numerical  Computation of Generalized  Averaged  Gaussian  and  Anti-Gauss  Quadrature  Rules",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7217"
}

Spalević, M.. (2023). Numerical  Computation of Generalized  Averaged  Gaussian  and  Anti-Gauss  Quadrature  Rules. in 6th International Conference on Mathematics and Related Sciences (ICMRS 2023), online meeting,  Turkey.
https://hdl.handle.net/21.15107/rcub_machinery_7217

Spalević M. Numerical  Computation of Generalized  Averaged  Gaussian  and  Anti-Gauss  Quadrature  Rules. in 6th International Conference on Mathematics and Related Sciences (ICMRS 2023), online meeting,  Turkey. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7217 .

Spalević, Miodrag, "Numerical  Computation of Generalized  Averaged  Gaussian  and  Anti-Gauss  Quadrature  Rules" in 6th International Conference on Mathematics and Related Sciences (ICMRS 2023), online meeting,  Turkey (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7217 .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2023
UR  - http://acmij.az/view.php?lang=az&menu=0
UR  - http://acmij.az/view.php?lang=az&menu=journal&id=624
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7380
AB  - The internality of quadrature rules, i.e., the property that all nodes lie in the interior of the convex hull of the support of the measure, is important in applications, because this allows the application of these quadrature rules to the approximation of integrals with integrands that are defined in the convex hull of the support of the measure only. It is known that the averaged Gauss and optimal averaged Gauss quadrature rules with respect to the four Chebyshev measures modified by a linear divisor are internal. This paper investigates the internality of similarly modified Jacobi measures, namely measures defined by weight functions. With a, b > −1 and z ∈ R, |z| > 1. We will show that in some cases, depending on the exponents a and b, the averaged and optimal averaged Gauss rules for these measures are internal if the number of nodes is large enough.
PB  - Ministry of Communications and Information Technology (Azerbaijan), Azerbaijan National Academy of Sciences and Institute of Applied Mathematics of Baku State University
T2  - Applied and Computational Mathematics
T1  - Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures
EP  - 442
IS  - 4
SP  - 426
VL  - 22
DO  - 10.30546/1683-6154.22.4.2023.426
ER  - 

@article{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2023",
abstract = "The internality of quadrature rules, i.e., the property that all nodes lie in the interior of the convex hull of the support of the measure, is important in applications, because this allows the application of these quadrature rules to the approximation of integrals with integrands that are defined in the convex hull of the support of the measure only. It is known that the averaged Gauss and optimal averaged Gauss quadrature rules with respect to the four Chebyshev measures modified by a linear divisor are internal. This paper investigates the internality of similarly modified Jacobi measures, namely measures defined by weight functions. With a, b > −1 and z ∈ R, |z| > 1. We will show that in some cases, depending on the exponents a and b, the averaged and optimal averaged Gauss rules for these measures are internal if the number of nodes is large enough.",
publisher = "Ministry of Communications and Information Technology (Azerbaijan), Azerbaijan National Academy of Sciences and Institute of Applied Mathematics of Baku State University",
journal = "Applied and Computational Mathematics",
title = "Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures",
pages = "442-426",
number = "4",
volume = "22",
doi = "10.30546/1683-6154.22.4.2023.426"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2023). Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures. in Applied and Computational Mathematics
Ministry of Communications and Information Technology (Azerbaijan), Azerbaijan National Academy of Sciences and Institute of Applied Mathematics of Baku State University., 22(4), 426-442.
https://doi.org/10.30546/1683-6154.22.4.2023.426

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures. in Applied and Computational Mathematics. 2023;22(4):426-442.
doi:10.30546/1683-6154.22.4.2023.426 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures" in Applied and Computational Mathematics, 22, no. 4 (2023):426-442,
https://doi.org/10.30546/1683-6154.22.4.2023.426 . .

TY  - CONF
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2023
UR  - http://www.ic-mrs.org/
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7662
AB  - The averaged and optimal averaged quadrature rules provide a convenient method of approximating the error in the Gauss quadrature. However, they are fully applicable only if their nodes are internal. We discuss two approaches to determine averaged quadrature rules with internal nodes: (i) truncating the Jacobi matrix associated with the optimal averaged rule, and (ii) weighting the optimal averaged quadrature rule. A survey of our results on internality of averaged Gaussian quadrature rules will be presented.
C3  - 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS
T1  - Internality of Averaged Gaussian Quadrature Rules
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7662
ER  - 

@conference{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2023",
abstract = "The averaged and optimal averaged quadrature rules provide a convenient method of approximating the error in the Gauss quadrature. However, they are fully applicable only if their nodes are internal. We discuss two approaches to determine averaged quadrature rules with internal nodes: (i) truncating the Jacobi matrix associated with the optimal averaged rule, and (ii) weighting the optimal averaged quadrature rule. A survey of our results on internality of averaged Gaussian quadrature rules will be presented.",
journal = "6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS",
title = "Internality of Averaged Gaussian Quadrature Rules",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7662"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2023). Internality of Averaged Gaussian Quadrature Rules. in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS.
https://hdl.handle.net/21.15107/rcub_machinery_7662

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Internality of Averaged Gaussian Quadrature Rules. in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7662 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Internality of Averaged Gaussian Quadrature Rules" in 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES  BOOK OF ABSTRACTS (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7662 .

TY  - CONF
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2023
UR  - https://imi.pmf.kg.ac.rs/aaa2023/
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7216
PB  - Prirodno-matematički fakultet Kragujevac
C3  - International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja
T1  - On Internality of Generalized Averaged Gaussian Quadrature Rules and Their Truncations
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7216
ER  - 

@conference{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2023",
publisher = "Prirodno-matematički fakultet Kragujevac",
journal = "International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja",
title = "On Internality of Generalized Averaged Gaussian Quadrature Rules and Their Truncations",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7216"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2023). On Internality of Generalized Averaged Gaussian Quadrature Rules and Their Truncations. in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja
Prirodno-matematički fakultet Kragujevac..
https://hdl.handle.net/21.15107/rcub_machinery_7216

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. On Internality of Generalized Averaged Gaussian Quadrature Rules and Their Truncations. in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7216 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "On Internality of Generalized Averaged Gaussian Quadrature Rules and Their Truncations" in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7216 .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5111
PB  - Springer
T2  - Numerical Algorithms
T1  - Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds
EP  - 544
SP  - 523
VL  - 92
DO  - 10.1007/s11075-022-01385-w
ER  - 

@article{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2023",
publisher = "Springer",
journal = "Numerical Algorithms",
title = "Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds",
pages = "544-523",
volume = "92",
doi = "10.1007/s11075-022-01385-w"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2023). Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds. in Numerical Algorithms
Springer., 92, 523-544.
https://doi.org/10.1007/s11075-022-01385-w

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds. in Numerical Algorithms. 2023;92:523-544.
doi:10.1007/s11075-022-01385-w .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds" in Numerical Algorithms, 92 (2023):523-544,
https://doi.org/10.1007/s11075-022-01385-w . .

Spalević, M., Aranđelović, I., Pejčev, A., Đukić, D., Tomanović, J.,& Mutavdžić Đukić, R.. (2023). Višestruki, krivolinijski i površinski integrali. in Univerzitet u Beogradu - Mašinski fakultet
Univerzitet u Beogradu - Mašinski fakultet..
https://hdl.handle.net/21.15107/rcub_machinery_7221

Spalević M, Aranđelović I, Pejčev A, Đukić D, Tomanović J, Mutavdžić Đukić R. Višestruki, krivolinijski i površinski integrali. in Univerzitet u Beogradu - Mašinski fakultet. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7221 .

Spalević, Miodrag, Aranđelović, Ivan, Pejčev, Aleksandar, Đukić, Dušan, Tomanović, Jelena, Mutavdžić Đukić, Rada, "Višestruki, krivolinijski i površinski integrali" in Univerzitet u Beogradu - Mašinski fakultet (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7221 .

Spalević, M.. (2023). ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. 
Kent State University..
https://hdl.handle.net/21.15107/rcub_machinery_7218

Spalević M. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7218 .

Spalević, Miodrag, "ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS" (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7218 .

TY  - CONF
AU  - Jandrlić, Davorka
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7215
PB  - Prirodno-matematički fakultet Kragujevac
C3  - International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja
T1  - Error estimates for Gaussian quadrature formulae
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7215
ER  - 

@conference{
author = "Jandrlić, Davorka and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2023",
publisher = "Prirodno-matematički fakultet Kragujevac",
journal = "International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja",
title = "Error estimates for Gaussian quadrature formulae",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7215"
}

Jandrlić, D., Pejčev, A.,& Spalević, M.. (2023). Error estimates for Gaussian quadrature formulae. in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja
Prirodno-matematički fakultet Kragujevac..
https://hdl.handle.net/21.15107/rcub_machinery_7215

Jandrlić D, Pejčev A, Spalević M. Error estimates for Gaussian quadrature formulae. in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7215 .

Jandrlić, Davorka, Pejčev, Aleksandar, Spalević, Miodrag, "Error estimates for Gaussian quadrature formulae" in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7215 .

TY  - GEN
AU  - Spalević, Miodrag
AU  - Stanić, Marija
PY  - 2023
UR  - https://imi.pmf.kg.ac.rs/aaa2023/
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7214
PB  - Prirodno-matematički fakultet Kragujevac
T2  - International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja
T1  - The life path and scientific career o fAcademician Professor Gradimir V. Milovanović
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7214
ER  - 

@misc{
author = "Spalević, Miodrag and Stanić, Marija",
year = "2023",
publisher = "Prirodno-matematički fakultet Kragujevac",
journal = "International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja",
title = "The life path and scientific career o fAcademician Professor Gradimir V. Milovanović",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7214"
}

Spalević, M.,& Stanić, M.. (2023). The life path and scientific career o fAcademician Professor Gradimir V. Milovanović. in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja
Prirodno-matematički fakultet Kragujevac..
https://hdl.handle.net/21.15107/rcub_machinery_7214

Spalević M, Stanić M. The life path and scientific career o fAcademician Professor Gradimir V. Milovanović. in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja. 2023;.
https://hdl.handle.net/21.15107/rcub_machinery_7214 .

Spalević, Miodrag, Stanić, Marija, "The life path and scientific career o fAcademician Professor Gradimir V. Milovanović" in International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja (2023),
https://hdl.handle.net/21.15107/rcub_machinery_7214 .

TY  - JOUR
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3685
AB  - The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing. Laurie developed anti-Gauss quadrature rules as an aid to estimate this error. Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower bounds for the value of the desired integral. It is then natural to use the average of Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also introduced these averaged rules. More recently, Spalevic derived new averaged Gauss quadrature rules that have higher degree of exactness for the same number of nodes as the averaged rules proposed by Laurie. Numerical experiments reported in this paper show both kinds of averaged rules to often give much higher accuracy than can be expected from their degrees of exactness. This is important when estimating the error in a Gauss rule by an associated averaged rule. We use techniques similar to those employed by Trefethen in his investigation of Clenshaw-Curtis rules to shed light on the performance of the averaged rules. The averaged rules are not guaranteed to be internal, i.e., they may have nodes outside the convex hull of the support of the measure. This paper discusses three approaches to modify averaged rules to make them internal.
PB  - Elsevier, Amsterdam
T2  - Journal of Computational and Applied Mathematics
T1  - Averaged Gauss quadrature formulas: Properties and applications
VL  - 410
DO  - 10.1016/j.cam.2022.114232
ER  - 

@article{
author = "Reichel, Lothar and Spalević, Miodrag",
year = "2022",
abstract = "The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing. Laurie developed anti-Gauss quadrature rules as an aid to estimate this error. Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower bounds for the value of the desired integral. It is then natural to use the average of Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also introduced these averaged rules. More recently, Spalevic derived new averaged Gauss quadrature rules that have higher degree of exactness for the same number of nodes as the averaged rules proposed by Laurie. Numerical experiments reported in this paper show both kinds of averaged rules to often give much higher accuracy than can be expected from their degrees of exactness. This is important when estimating the error in a Gauss rule by an associated averaged rule. We use techniques similar to those employed by Trefethen in his investigation of Clenshaw-Curtis rules to shed light on the performance of the averaged rules. The averaged rules are not guaranteed to be internal, i.e., they may have nodes outside the convex hull of the support of the measure. This paper discusses three approaches to modify averaged rules to make them internal.",
publisher = "Elsevier, Amsterdam",
journal = "Journal of Computational and Applied Mathematics",
title = "Averaged Gauss quadrature formulas: Properties and applications",
volume = "410",
doi = "10.1016/j.cam.2022.114232"
}

Reichel, L.,& Spalević, M.. (2022). Averaged Gauss quadrature formulas: Properties and applications. in Journal of Computational and Applied Mathematics
Elsevier, Amsterdam., 410.
https://doi.org/10.1016/j.cam.2022.114232

Reichel L, Spalević M. Averaged Gauss quadrature formulas: Properties and applications. in Journal of Computational and Applied Mathematics. 2022;410.
doi:10.1016/j.cam.2022.114232 .

Reichel, Lothar, Spalević, Miodrag, "Averaged Gauss quadrature formulas: Properties and applications" in Journal of Computational and Applied Mathematics, 410 (2022),
https://doi.org/10.1016/j.cam.2022.114232 . .

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  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5153
C3  - FAATNA 2020>22 conference, Book of abstracts
T1  - Internality of averaged Gaussian quadrature rules for modified Jacobi measures
EP  - 193
SP  - 193
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5153
ER  - 

@conference{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2022",
journal = "FAATNA 2020>22 conference, Book of abstracts",
title = "Internality of averaged Gaussian quadrature rules for modified Jacobi measures",
pages = "193-193",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5153"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2022). Internality of averaged Gaussian quadrature rules for modified Jacobi measures. in FAATNA 2020>22 conference, Book of abstracts, 193-193.
https://hdl.handle.net/21.15107/rcub_machinery_5153

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Internality of averaged Gaussian quadrature rules for modified Jacobi measures. in FAATNA 2020>22 conference, Book of abstracts. 2022;:193-193.
https://hdl.handle.net/21.15107/rcub_machinery_5153 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Internality of averaged Gaussian quadrature rules for modified Jacobi measures" in FAATNA 2020>22 conference, Book of abstracts (2022):193-193,
https://hdl.handle.net/21.15107/rcub_machinery_5153 .

TY  - CONF
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5159
PB  - Faculty of Mechanical Engineering, University of Belgrade
C3  - NMLSP conference, Book of abstracts
T1  - Optimal averaged Pade approximants
EP  - 65
SP  - 65
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5159
ER  - 

@conference{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2022",
publisher = "Faculty of Mechanical Engineering, University of Belgrade",
journal = "NMLSP conference, Book of abstracts",
title = "Optimal averaged Pade approximants",
pages = "65-65",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5159"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2022). Optimal averaged Pade approximants. in NMLSP conference, Book of abstracts
Faculty of Mechanical Engineering, University of Belgrade., 65-65.
https://hdl.handle.net/21.15107/rcub_machinery_5159

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Optimal averaged Pade approximants. in NMLSP conference, Book of abstracts. 2022;:65-65.
https://hdl.handle.net/21.15107/rcub_machinery_5159 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Optimal averaged Pade approximants" in NMLSP conference, Book of abstracts (2022):65-65,
https://hdl.handle.net/21.15107/rcub_machinery_5159 .

TY  - CONF
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5155
C3  - FAATNA 2020>22, Book of abstarcts
T1  - Weighted averaged Gaussian quadrature rules for modified Chebyshev measure
EP  - 197
SP  - 197
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5155
ER  - 

@conference{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2022",
journal = "FAATNA 2020>22, Book of abstarcts",
title = "Weighted averaged Gaussian quadrature rules for modified Chebyshev measure",
pages = "197-197",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5155"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2022). Weighted averaged Gaussian quadrature rules for modified Chebyshev measure. in FAATNA 2020>22, Book of abstarcts, 197-197.
https://hdl.handle.net/21.15107/rcub_machinery_5155

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Weighted averaged Gaussian quadrature rules for modified Chebyshev measure. in FAATNA 2020>22, Book of abstarcts. 2022;:197-197.
https://hdl.handle.net/21.15107/rcub_machinery_5155 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Weighted averaged Gaussian quadrature rules for modified Chebyshev measure" in FAATNA 2020>22, Book of abstarcts (2022):197-197,
https://hdl.handle.net/21.15107/rcub_machinery_5155 .

TY  - CONF
AU  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5162
PB  - Faculty of Mechanical Engineering, University of Belgrade
C3  - MNA conference, Book of abstracts
T1  - Weighted averaged Gaussian quadrature rules for modified Chebyshev measure
EP  - 19
SP  - 19
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5162
ER  - 

@conference{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2022",
publisher = "Faculty of Mechanical Engineering, University of Belgrade",
journal = "MNA conference, Book of abstracts",
title = "Weighted averaged Gaussian quadrature rules for modified Chebyshev measure",
pages = "19-19",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5162"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2022). Weighted averaged Gaussian quadrature rules for modified Chebyshev measure. in MNA conference, Book of abstracts
Faculty of Mechanical Engineering, University of Belgrade., 19-19.
https://hdl.handle.net/21.15107/rcub_machinery_5162

Đukić D, Mutavdžić Đukić R, Reichel L, Spalević M. Weighted averaged Gaussian quadrature rules for modified Chebyshev measure. in MNA conference, Book of abstracts. 2022;:19-19.
https://hdl.handle.net/21.15107/rcub_machinery_5162 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Reichel, Lothar, Spalević, Miodrag, "Weighted averaged Gaussian quadrature rules for modified Chebyshev measure" in MNA conference, Book of abstracts (2022):19-19,
https://hdl.handle.net/21.15107/rcub_machinery_5162 .

TY  - CONF
AU  - Jandrlić, Davorka
AU  - Krtinić, Đorđe
AU  - Mihić, Ljubica
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/5161
PB  - Faculty of Mechanical Engineering, University of Belgrade
C3  - MNA conference, Book of abstracts
T1  - Numerical evaluation of the error term in Gaussian quadrature with the Legendre weight function
EP  - 13
SP  - 13
UR  - https://hdl.handle.net/21.15107/rcub_machinery_5161
ER  - 

@conference{
author = "Jandrlić, Davorka and Krtinić, Đorđe and Mihić, Ljubica and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2022",
publisher = "Faculty of Mechanical Engineering, University of Belgrade",
journal = "MNA conference, Book of abstracts",
title = "Numerical evaluation of the error term in Gaussian quadrature with the Legendre weight function",
pages = "13-13",
url = "https://hdl.handle.net/21.15107/rcub_machinery_5161"
}

Jandrlić, D., Krtinić, Đ., Mihić, L., Pejčev, A.,& Spalević, M.. (2022). Numerical evaluation of the error term in Gaussian quadrature with the Legendre weight function. in MNA conference, Book of abstracts
Faculty of Mechanical Engineering, University of Belgrade., 13-13.
https://hdl.handle.net/21.15107/rcub_machinery_5161

Jandrlić D, Krtinić Đ, Mihić L, Pejčev A, Spalević M. Numerical evaluation of the error term in Gaussian quadrature with the Legendre weight function. in MNA conference, Book of abstracts. 2022;:13-13.
https://hdl.handle.net/21.15107/rcub_machinery_5161 .

Jandrlić, Davorka, Krtinić, Đorđe, Mihić, Ljubica, Pejčev, Aleksandar, Spalević, Miodrag, "Numerical evaluation of the error term in Gaussian quadrature with the Legendre weight function" in MNA conference, Book of abstracts (2022):13-13,
https://hdl.handle.net/21.15107/rcub_machinery_5161 .