Error estimates of Gauss-type quadrature rules for variable-sign weight functions
Апстракт
The n-point Gauss quadrature formula Gn is known to be a unique optimal interpolatory quadrature rule. In practical applications of Gn, it is important to be able to estimate its error. For that purpose, (2n+1)-point extensions that inherit the n nodes of Gn, such as the Gauss-Kronrod, averaged Gauss, and generalized averaged Gauss quadrature rules, can be used. When Gn is applied, the weight function (or the measure) is usually assumed to be non-negative on the integration interval. In the present paper, we consider the recently introduced n-point Gauss-type quadrature formula Qn with respect to weight functions that change the sign in the interior of the integration interval. To estimate the error of Qn, we construct its (2n+1)-point extensions that inherit the n nodes of Qn and that are analogous to the Gauss-Kronrod, averaged Gauss, and generalized averaged Gauss quadrature rules. Numerical examples illustrate the accuracy of the error estimates obtained by these extensions.
Извор:
ICMRS 2023, Book of abstracts, 2023Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Tomanović, Jelena PY - 2023 UR - https://machinery.mas.bg.ac.rs/handle/123456789/7220 AB - The n-point Gauss quadrature formula Gn is known to be a unique optimal interpolatory quadrature rule. In practical applications of Gn, it is important to be able to estimate its error. For that purpose, (2n+1)-point extensions that inherit the n nodes of Gn, such as the Gauss-Kronrod, averaged Gauss, and generalized averaged Gauss quadrature rules, can be used. When Gn is applied, the weight function (or the measure) is usually assumed to be non-negative on the integration interval. In the present paper, we consider the recently introduced n-point Gauss-type quadrature formula Qn with respect to weight functions that change the sign in the interior of the integration interval. To estimate the error of Qn, we construct its (2n+1)-point extensions that inherit the n nodes of Qn and that are analogous to the Gauss-Kronrod, averaged Gauss, and generalized averaged Gauss quadrature rules. Numerical examples illustrate the accuracy of the error estimates obtained by these extensions. C3 - ICMRS 2023, Book of abstracts T1 - Error estimates of Gauss-type quadrature rules for variable-sign weight functions UR - https://hdl.handle.net/21.15107/rcub_machinery_7220 ER -
@conference{ author = "Tomanović, Jelena", year = "2023", abstract = "The n-point Gauss quadrature formula Gn is known to be a unique optimal interpolatory quadrature rule. In practical applications of Gn, it is important to be able to estimate its error. For that purpose, (2n+1)-point extensions that inherit the n nodes of Gn, such as the Gauss-Kronrod, averaged Gauss, and generalized averaged Gauss quadrature rules, can be used. When Gn is applied, the weight function (or the measure) is usually assumed to be non-negative on the integration interval. In the present paper, we consider the recently introduced n-point Gauss-type quadrature formula Qn with respect to weight functions that change the sign in the interior of the integration interval. To estimate the error of Qn, we construct its (2n+1)-point extensions that inherit the n nodes of Qn and that are analogous to the Gauss-Kronrod, averaged Gauss, and generalized averaged Gauss quadrature rules. Numerical examples illustrate the accuracy of the error estimates obtained by these extensions.", journal = "ICMRS 2023, Book of abstracts", title = "Error estimates of Gauss-type quadrature rules for variable-sign weight functions", url = "https://hdl.handle.net/21.15107/rcub_machinery_7220" }
Tomanović, J.. (2023). Error estimates of Gauss-type quadrature rules for variable-sign weight functions. in ICMRS 2023, Book of abstracts. https://hdl.handle.net/21.15107/rcub_machinery_7220
Tomanović J. Error estimates of Gauss-type quadrature rules for variable-sign weight functions. in ICMRS 2023, Book of abstracts. 2023;. https://hdl.handle.net/21.15107/rcub_machinery_7220 .
Tomanović, Jelena, "Error estimates of Gauss-type quadrature rules for variable-sign weight functions" in ICMRS 2023, Book of abstracts (2023), https://hdl.handle.net/21.15107/rcub_machinery_7220 .