Gauss-type quadrature rules for variable-sign weight functions
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| Názov: | Gauss-type quadrature rules for variable-sign weight functions |
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| Autori: | Tomanović, Jelena |
| Zdroj: | Challenges and Advances in Numerical Analysis Cagliari, Italy, June 5-9, 2023 CANA23, Book of abstracts |
| Rok vydania: | 2024 |
| Predmety: | Gauss quadrature rule, Variable-sign weight function, Modifier function, Vandermonde matrix, Maximum norm |
| Popis: | When the Gauss quadrature formula $G_n$ is applied, it is usually assumed that the weight function (or the measure) is non-negative on the integration interval $[a,b]$. In the present paper, we introduce a Gauss-type quadrature formula $Q_n$ for weight functions that change the sign in the interior of $[a,b]$. It proves that all nodes of $Q_n$ are pairwise distinct and contained in the interior of $[a,b]$. Moreover, $G_n$ (with a non-negative weight function) turns out to be a special case of $Q_n$. Obtained results on the remainder term of $Q_n$ suggest that the application of $Q_n$ makes sense both when the points from the interior of $[a,b]$ at which the weight function changes sign are known exactly, as well as when those points are known approximately. The accuracy of $Q_n$ is confirmed by numerical examples. |
| Druh dokumentu: | conference object |
| Jazyk: | English |
| Relation: | https://machinery.mas.bg.ac.rs/handle/123456789/7847; http://machinery.mas.bg.ac.rs/bitstream/id/19781/Tomanovic.pdf; https://hdl.handle.net/21.15107/rcub_machinery_7847 |
| Dostupnosť: | https://hdl.handle.net/21.15107/rcub_machinery_7847 https://machinery.mas.bg.ac.rs/handle/123456789/7847 http://machinery.mas.bg.ac.rs/bitstream/id/19781/Tomanovic.pdf |
| Rights: | openAccess ; https://creativecommons.org/licenses/by-nc-sa/4.0/ ; BY-NC-SA |
| Prístupové číslo: | edsbas.471BF333 |
| Databáza: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | When the Gauss quadrature formula $G_n$ is applied, it is usually assumed that the weight function (or the measure) is non-negative on the integration interval $[a,b]$. In the present paper, we introduce a Gauss-type quadrature formula $Q_n$ for weight functions that change the sign in the interior of $[a,b]$. It proves that all nodes of $Q_n$ are pairwise distinct and contained in the interior of $[a,b]$. Moreover, $G_n$ (with a non-negative weight function) turns out to be a special case of $Q_n$. Obtained results on the remainder term of $Q_n$ suggest that the application of $Q_n$ makes sense both when the points from the interior of $[a,b]$ at which the weight function changes sign are known exactly, as well as when those points are known approximately. The accuracy of $Q_n$ is confirmed by numerical examples. |
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