Rational Averaged Gauss Quadrature Rules
Apstrakt
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.
Ključne reči:
Rational generalized averaged Gauss quadrature / Rational averaged Gauss quadrature / Error estimations of rational Gauss quadratureIzvor:
Filomat, 2020, 34, 2, 379-389Izdavač:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Finansiranje / projekti:
- NSF grant DMS-1720259
- Ministarstvo nauke, tehnološkog razvoja i inovacija Republike Srbije, institucionalno finansiranje - 200105 (Univerzitet u Beogradu, Mašinski fakultet) (RS-MESTD-inst-2020-200105)
- NSF grant DMS-1729509
DOI: 10.2298/FIL2002379R
ISSN: 0354-5180
WoS: 000595329700011
Scopus: 2-s2.0-85096924468
Kolekcije
Institucija/grupa
Mašinski fakultetTY - 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 . .