Gauss-type quadrature rules for variable-sign weight functions
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| Titel: | Gauss-type quadrature rules for variable-sign weight functions |
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| Autoren: | Tomanović, Jelena |
| Quelle: | NASCA23, Book of abstracts |
| Publikationsjahr: | 2023 |
| Schlagwörter: | Gauss quadrature rule, Variable-sign weight function, Modifier function, Vandermonde matrix, Maximum norm |
| Beschreibung: | 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. |
| Publikationsart: | conference object |
| Sprache: | English |
| Relation: | https://machinery.mas.bg.ac.rs/handle/123456789/6962; https://hdl.handle.net/21.15107/rcub_machinery_6962 |
| Verfügbarkeit: | https://hdl.handle.net/21.15107/rcub_machinery_6962 https://machinery.mas.bg.ac.rs/handle/123456789/6962 |
| Rights: | openAccess ; https://creativecommons.org/licenses/by-nc-sa/4.0/ ; BY-NC-SA |
| Dokumentencode: | edsbas.BC39686C |
| Datenbank: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | 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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