TY  - JOUR
AU  - Reichel, Lothar
AU  - Spalević, Miodrag
AU  - Tomanović, Jelena
PY  - 2020
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3329
AB  - It is important to be able to estimate the quadrature error in Gauss rules. Several approaches have been developed, including the evaluation of associated Gauss-Kronrod rules (if they exist), or the associated averaged Gauss and generalized averaged Gauss rules. Integrals with certain integrands can be approximated more accurately by rational Gauss rules than by Gauss rules. This paper introduces associated rational averaged Gauss rules and rational generalized averaged Gauss rules, which can be used to estimate the error in rational Gauss rules. Also rational Gauss-Kronrod rules are discussed. Computed examples illustrate the accuracy of the error estimates determined by these quadrature rules.
PB  - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2  - Filomat
T1  - Rational Averaged Gauss Quadrature Rules
EP  - 389
IS  - 2
SP  - 379
VL  - 34
DO  - 10.2298/FIL2002379R
ER  - 

@article{
author = "Reichel, Lothar and Spalević, Miodrag and Tomanović, Jelena",
year = "2020",
abstract = "It is important to be able to estimate the quadrature error in Gauss rules. Several approaches have been developed, including the evaluation of associated Gauss-Kronrod rules (if they exist), or the associated averaged Gauss and generalized averaged Gauss rules. Integrals with certain integrands can be approximated more accurately by rational Gauss rules than by Gauss rules. This paper introduces associated rational averaged Gauss rules and rational generalized averaged Gauss rules, which can be used to estimate the error in rational Gauss rules. Also rational Gauss-Kronrod rules are discussed. Computed examples illustrate the accuracy of the error estimates determined by these quadrature rules.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "Rational Averaged Gauss Quadrature Rules",
pages = "389-379",
number = "2",
volume = "34",
doi = "10.2298/FIL2002379R"
}

Reichel, L., Spalević, M.,& Tomanović, J.. (2020). Rational Averaged Gauss Quadrature Rules. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 34(2), 379-389.
https://doi.org/10.2298/FIL2002379R

Reichel L, Spalević M, Tomanović J. Rational Averaged Gauss Quadrature Rules. in Filomat. 2020;34(2):379-389.
doi:10.2298/FIL2002379R .

Reichel, Lothar, Spalević, Miodrag, Tomanović, Jelena, "Rational Averaged Gauss Quadrature Rules" in Filomat, 34, no. 2 (2020):379-389,
https://doi.org/10.2298/FIL2002379R . .

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

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

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

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

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