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  - 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  - 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 .

TY  - JOUR
AU  - Đukić, Dušan
AU  - Fermo, Luisa
AU  - Mutavdžić Đukić, Rada
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3963
AB  - Stratified cubature rules are proposed to approximate double integrals defined on the real positive semiaxis. In particular, anti-Gauss cubature formulae are introduced and averaged cubature schemes are developed. Some of their appropriate modifications are also studied. Several numerical experiments are given to testify the performance of all the formulae.
PB  - Springer
T2  - Numerical Algorithms
T1  - Averaged cubature schemes on the real positive semiaxis
VL  - 92, 545–569
DO  - 10.1007/s11075-022-01408-6
ER  - 

@article{
author = "Đukić, Dušan and Fermo, Luisa and Mutavdžić Đukić, Rada",
year = "2022",
abstract = "Stratified cubature rules are proposed to approximate double integrals defined on the real positive semiaxis. In particular, anti-Gauss cubature formulae are introduced and averaged cubature schemes are developed. Some of their appropriate modifications are also studied. Several numerical experiments are given to testify the performance of all the formulae.",
publisher = "Springer",
journal = "Numerical Algorithms",
title = "Averaged cubature schemes on the real positive semiaxis",
volume = "92, 545–569",
doi = "10.1007/s11075-022-01408-6"
}

Đukić, D., Fermo, L.,& Mutavdžić Đukić, R.. (2022). Averaged cubature schemes on the real positive semiaxis. in Numerical Algorithms
Springer., 92, 545–569.
https://doi.org/10.1007/s11075-022-01408-6

Đukić D, Fermo L, Mutavdžić Đukić R. Averaged cubature schemes on the real positive semiaxis. in Numerical Algorithms. 2022;92, 545–569.
doi:10.1007/s11075-022-01408-6 .

Đukić, Dušan, Fermo, Luisa, Mutavdžić Đukić, Rada, "Averaged cubature schemes on the real positive semiaxis" in Numerical Algorithms, 92, 545–569 (2022),
https://doi.org/10.1007/s11075-022-01408-6 . .

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  - GEN
AU  - Đukić, Dušan
AU  - Pejčev, Aleksandar
AU  - Tomanović, Jelena
AU  - Mutavdžić Đukić, Rada
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6238
PB  - Univerzitet u Beogradu - Mašinski fakultet
T2  - Univerzitet u Beogradu - Mašinski fakultet
T1  - Zbirka zadataka za pripremu kvalifikacionog ispita za upis na Mašinski fakultet u Beogradu
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6238
ER  - 

@misc{
author = "Đukić, Dušan and Pejčev, Aleksandar and Tomanović, Jelena and Mutavdžić Đukić, Rada",
year = "2022",
publisher = "Univerzitet u Beogradu - Mašinski fakultet",
journal = "Univerzitet u Beogradu - Mašinski fakultet",
title = "Zbirka zadataka za pripremu kvalifikacionog ispita za upis na Mašinski fakultet u Beogradu",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6238"
}

Đukić, D., Pejčev, A., Tomanović, J.,& Mutavdžić Đukić, R.. (2022). Zbirka zadataka za pripremu kvalifikacionog ispita za upis na Mašinski fakultet u Beogradu. in Univerzitet u Beogradu - Mašinski fakultet
Univerzitet u Beogradu - Mašinski fakultet..
https://hdl.handle.net/21.15107/rcub_machinery_6238

Đukić D, Pejčev A, Tomanović J, Mutavdžić Đukić R. Zbirka zadataka za pripremu kvalifikacionog ispita za upis na Mašinski fakultet u Beogradu. in Univerzitet u Beogradu - Mašinski fakultet. 2022;.
https://hdl.handle.net/21.15107/rcub_machinery_6238 .

Đukić, Dušan, Pejčev, Aleksandar, Tomanović, Jelena, Mutavdžić Đukić, Rada, "Zbirka zadataka za pripremu kvalifikacionog ispita za upis na Mašinski fakultet u Beogradu" in Univerzitet u Beogradu - Mašinski fakultet (2022),
https://hdl.handle.net/21.15107/rcub_machinery_6238 .

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  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3477
AB  - It is desirable that a quadrature rule be internal, i.e., that all nodes of the rule live in the convex hull of the support of the measure. Then the rule can be applied to approximate integrals of functions that have a singularity close to the convex hull of the support of the measure. This paper investigates whether generalized averaged Gauss quadrature formulas for modified Chebyshev measures of the first kind are internal. These rules are applied to estimate the error in Gauss quadrature rules associated with modified Chebyshev measures of the first kind. It is of considerable interest to be able to assess the error in quadrature rules in order to be able to choose a rule that gives an approximation of the desired integral of sufficient accuracy without having to evaluate the integrand at unnecessarily many nodes. Some of the generalized averaged Gauss quadrature formulas considered are found not to be internal. We will show that some truncated variants of these rules are internal, and therefore can be applied to estimate the error in Gauss quadrature rules also when the integrand has singularities on the real axis close to the interval of integration.
PB  - Elsevier, Amsterdam
T2  - Journal of Computational and Applied Mathematics
T1  - Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind
VL  - 398
DO  - 10.1016/j.cam.2021.113696
ER  - 

@article{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Reichel, Lothar and Spalević, Miodrag",
year = "2021",
abstract = "It is desirable that a quadrature rule be internal, i.e., that all nodes of the rule live in the convex hull of the support of the measure. Then the rule can be applied to approximate integrals of functions that have a singularity close to the convex hull of the support of the measure. This paper investigates whether generalized averaged Gauss quadrature formulas for modified Chebyshev measures of the first kind are internal. These rules are applied to estimate the error in Gauss quadrature rules associated with modified Chebyshev measures of the first kind. It is of considerable interest to be able to assess the error in quadrature rules in order to be able to choose a rule that gives an approximation of the desired integral of sufficient accuracy without having to evaluate the integrand at unnecessarily many nodes. Some of the generalized averaged Gauss quadrature formulas considered are found not to be internal. We will show that some truncated variants of these rules are internal, and therefore can be applied to estimate the error in Gauss quadrature rules also when the integrand has singularities on the real axis close to the interval of integration.",
publisher = "Elsevier, Amsterdam",
journal = "Journal of Computational and Applied Mathematics",
title = "Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind",
volume = "398",
doi = "10.1016/j.cam.2021.113696"
}

Đukić, D., Mutavdžić Đukić, R., Reichel, L.,& Spalević, M.. (2021). Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind. in Journal of Computational and Applied Mathematics
Elsevier, Amsterdam., 398.
https://doi.org/10.1016/j.cam.2021.113696

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 first kind. in Journal of Computational and Applied Mathematics. 2021;398.
doi:10.1016/j.cam.2021.113696 .

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 first kind" in Journal of Computational and Applied Mathematics, 398 (2021),
https://doi.org/10.1016/j.cam.2021.113696 . .

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  - Đukić, Dušan
AU  - Mutavdžić Đukić, Rada
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3260
AB  - This paper presents a survey of recent results on error estimates of Gaussian-type quadrature formulas for analytic functions on confocal ellipses.
PB  - Kent State University, Kent
T2  - Electronic Transactions on Numerical Analysis
T1  - Error estimates of gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results
EP  - 382
SP  - 352
VL  - 53
DO  - 10.1553/etna_vol53s352
ER  - 

@article{
author = "Đukić, Dušan and Mutavdžić Đukić, Rada and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2020",
abstract = "This paper presents a survey of recent results on error estimates of Gaussian-type quadrature formulas for analytic functions on confocal ellipses.",
publisher = "Kent State University, Kent",
journal = "Electronic Transactions on Numerical Analysis",
title = "Error estimates of gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results",
pages = "382-352",
volume = "53",
doi = "10.1553/etna_vol53s352"
}

Đukić, D., Mutavdžić Đukić, R., Pejčev, A.,& Spalević, M.. (2020). Error estimates of gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results. in Electronic Transactions on Numerical Analysis
Kent State University, Kent., 53, 352-382.
https://doi.org/10.1553/etna_vol53s352

Đukić D, Mutavdžić Đukić R, Pejčev A, Spalević M. Error estimates of gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results. in Electronic Transactions on Numerical Analysis. 2020;53:352-382.
doi:10.1553/etna_vol53s352 .

Đukić, Dušan, Mutavdžić Đukić, Rada, Pejčev, Aleksandar, Spalević, Miodrag, "Error estimates of gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results" in Electronic Transactions on Numerical Analysis, 53 (2020):352-382,
https://doi.org/10.1553/etna_vol53s352 . .

TY  - BOOK
AU  - Aranđelović, Ivan
AU  - Pejčev, Aleksandar
AU  - Đukić, Dušan
AU  - Jandrlić, Davorka
AU  - Tomanović, Jelena
AU  - Mutavdžić Đukić, Rada
AU  - Vučić, Miloš
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6256
PB  - Univerzitet u Beogradu - Mašinski fakultet
T2  - Univerzitet u Beogradu - Mašinski fakultet
T1  - Matematika 1: udžbenik i zbirka zadataka
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6256
ER  - 

@book{
author = "Aranđelović, Ivan and Pejčev, Aleksandar and Đukić, Dušan and Jandrlić, Davorka and Tomanović, Jelena and Mutavdžić Đukić, Rada and Vučić, Miloš",
year = "2020",
publisher = "Univerzitet u Beogradu - Mašinski fakultet",
journal = "Univerzitet u Beogradu - Mašinski fakultet",
title = "Matematika 1: udžbenik i zbirka zadataka",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6256"
}

Aranđelović, I., Pejčev, A., Đukić, D., Jandrlić, D., Tomanović, J., Mutavdžić Đukić, R.,& Vučić, M.. (2020). Matematika 1: udžbenik i zbirka zadataka. in Univerzitet u Beogradu - Mašinski fakultet
Univerzitet u Beogradu - Mašinski fakultet..
https://hdl.handle.net/21.15107/rcub_machinery_6256

Aranđelović I, Pejčev A, Đukić D, Jandrlić D, Tomanović J, Mutavdžić Đukić R, Vučić M. Matematika 1: udžbenik i zbirka zadataka. in Univerzitet u Beogradu - Mašinski fakultet. 2020;.
https://hdl.handle.net/21.15107/rcub_machinery_6256 .

Aranđelović, Ivan, Pejčev, Aleksandar, Đukić, Dušan, Jandrlić, Davorka, Tomanović, Jelena, Mutavdžić Đukić, Rada, Vučić, Miloš, "Matematika 1: udžbenik i zbirka zadataka" in Univerzitet u Beogradu - Mašinski fakultet (2020),
https://hdl.handle.net/21.15107/rcub_machinery_6256 .

TY  - BOOK
AU  - Aranđelović, Ivan
AU  - Jandrlić, Davorka
AU  - Pejčev, Aleksandar
AU  - Đukić, Dušan
AU  - Tomanović, Jelena
AU  - Mutavdžić Đukić, Rada
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6260
PB  - Univerzitet u Beogradu - Mašinski fakultet
T2  - Univerzitet u Beogradu - Mašinski fakultet
T1  - Matematika 2
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6260
ER  - 

@book{
author = "Aranđelović, Ivan and Jandrlić, Davorka and Pejčev, Aleksandar and Đukić, Dušan and Tomanović, Jelena and Mutavdžić Đukić, Rada",
year = "2019",
publisher = "Univerzitet u Beogradu - Mašinski fakultet",
journal = "Univerzitet u Beogradu - Mašinski fakultet",
title = "Matematika 2",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6260"
}

Aranđelović, I., Jandrlić, D., Pejčev, A., Đukić, D., Tomanović, J.,& Mutavdžić Đukić, R.. (2019). Matematika 2. in Univerzitet u Beogradu - Mašinski fakultet
Univerzitet u Beogradu - Mašinski fakultet..
https://hdl.handle.net/21.15107/rcub_machinery_6260

Aranđelović I, Jandrlić D, Pejčev A, Đukić D, Tomanović J, Mutavdžić Đukić R. Matematika 2. in Univerzitet u Beogradu - Mašinski fakultet. 2019;.
https://hdl.handle.net/21.15107/rcub_machinery_6260 .

Aranđelović, Ivan, Jandrlić, Davorka, Pejčev, Aleksandar, Đukić, Dušan, Tomanović, Jelena, Mutavdžić Đukić, Rada, "Matematika 2" in Univerzitet u Beogradu - Mašinski fakultet (2019),
https://hdl.handle.net/21.15107/rcub_machinery_6260 .

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  - 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 . .