Error Estimates for Certain Cubature Formulae
Апстракт
We estimate the errors of selected cubature formulae constructed by the product of Gauss quadrature rules. The cases of multiple and (hyper-)surface integrals over n-dimensional cube, simplex, sphere and ball are considered. The error estimates are obtained as the absolute value of the difference between cubature formula constructed by the product of Gauss quadrature rules and cubature formula constructed by the product of corresponding Gauss-Kronrod or corresponding generalized averaged Gaussian quadrature rules. Generalized averaged Gaussian quadrature rule (G) over cap (2l+1) is (2l + 1)-point quadrature formula. It has 2l + 1 nodes and the nodes of the corresponding Gauss rule G(l) with l nodes form a subset, similar to the situation for the (2l + 1)-point Gauss-Kronrod rule H2l+1 associated with G(l). The advantages of (G) over cap (2l+1) are that it exists also when H2l+1 does not, and that the numerical construction of (G) over cap (2l+1), based on recently proposed effective nu...merical procedure, is simpler than the construction of H2l+1.
Кључне речи:
Product of Gaussian formulas / Generalized averaged Gaussian formulas / Cubature rulesИзвор:
Filomat, 2018, 32, 20, 6893-6902Издавач:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Финансирање / пројекти:
DOI: 10.2298/FIL1820893J
ISSN: 0354-5180
WoS: 000463447500005
Scopus: 2-s2.0-85061405180
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Jandrlić, Davorka AU - Spalević, Miodrag AU - Tomanović, Jelena PY - 2018 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2822 AB - We estimate the errors of selected cubature formulae constructed by the product of Gauss quadrature rules. The cases of multiple and (hyper-)surface integrals over n-dimensional cube, simplex, sphere and ball are considered. The error estimates are obtained as the absolute value of the difference between cubature formula constructed by the product of Gauss quadrature rules and cubature formula constructed by the product of corresponding Gauss-Kronrod or corresponding generalized averaged Gaussian quadrature rules. Generalized averaged Gaussian quadrature rule (G) over cap (2l+1) is (2l + 1)-point quadrature formula. It has 2l + 1 nodes and the nodes of the corresponding Gauss rule G(l) with l nodes form a subset, similar to the situation for the (2l + 1)-point Gauss-Kronrod rule H2l+1 associated with G(l). The advantages of (G) over cap (2l+1) are that it exists also when H2l+1 does not, and that the numerical construction of (G) over cap (2l+1), based on recently proposed effective numerical procedure, is simpler than the construction of H2l+1. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - Error Estimates for Certain Cubature Formulae EP - 6902 IS - 20 SP - 6893 VL - 32 DO - 10.2298/FIL1820893J ER -
@article{ author = "Jandrlić, Davorka and Spalević, Miodrag and Tomanović, Jelena", year = "2018", abstract = "We estimate the errors of selected cubature formulae constructed by the product of Gauss quadrature rules. The cases of multiple and (hyper-)surface integrals over n-dimensional cube, simplex, sphere and ball are considered. The error estimates are obtained as the absolute value of the difference between cubature formula constructed by the product of Gauss quadrature rules and cubature formula constructed by the product of corresponding Gauss-Kronrod or corresponding generalized averaged Gaussian quadrature rules. Generalized averaged Gaussian quadrature rule (G) over cap (2l+1) is (2l + 1)-point quadrature formula. It has 2l + 1 nodes and the nodes of the corresponding Gauss rule G(l) with l nodes form a subset, similar to the situation for the (2l + 1)-point Gauss-Kronrod rule H2l+1 associated with G(l). The advantages of (G) over cap (2l+1) are that it exists also when H2l+1 does not, and that the numerical construction of (G) over cap (2l+1), based on recently proposed effective numerical procedure, is simpler than the construction of H2l+1.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "Error Estimates for Certain Cubature Formulae", pages = "6902-6893", number = "20", volume = "32", doi = "10.2298/FIL1820893J" }
Jandrlić, D., Spalević, M.,& Tomanović, J.. (2018). Error Estimates for Certain Cubature Formulae. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 32(20), 6893-6902. https://doi.org/10.2298/FIL1820893J
Jandrlić D, Spalević M, Tomanović J. Error Estimates for Certain Cubature Formulae. in Filomat. 2018;32(20):6893-6902. doi:10.2298/FIL1820893J .
Jandrlić, Davorka, Spalević, Miodrag, Tomanović, Jelena, "Error Estimates for Certain Cubature Formulae" in Filomat, 32, no. 20 (2018):6893-6902, https://doi.org/10.2298/FIL1820893J . .