Rational Averaged Gauss Quadrature Rules
Апстракт
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.
Кључне речи:
Rational generalized averaged Gauss quadrature / Rational averaged Gauss quadrature / Error estimations of rational Gauss quadratureИзвор:
Filomat, 2020, 34, 2, 379-389Издавач:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Финансирање / пројекти:
- NSF grant DMS-1720259
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
- NSF grant DMS-1729509
DOI: 10.2298/FIL2002379R
ISSN: 0354-5180
WoS: 000595329700011
Scopus: 2-s2.0-85096924468
Колекције
Институција/група
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 . .