Gauss-type quadrature rules for variable-sign weight functions
Апстракт
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.
Кључне речи:
Gauss quadrature rule / Variable-sign weight function / Modifier function / Vandermonde matrix / Maximum normИзвор:
NASCA23, Book of abstracts, 2023Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Tomanović, Jelena PY - 2023 UR - https://machinery.mas.bg.ac.rs/handle/123456789/6962 AB - 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. C3 - NASCA23, Book of abstracts T1 - Gauss-type quadrature rules for variable-sign weight functions UR - https://hdl.handle.net/21.15107/rcub_machinery_6962 ER -
@conference{ author = "Tomanović, Jelena", year = "2023", 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.", journal = "NASCA23, Book of abstracts", title = "Gauss-type quadrature rules for variable-sign weight functions", url = "https://hdl.handle.net/21.15107/rcub_machinery_6962" }
Tomanović, J.. (2023). Gauss-type quadrature rules for variable-sign weight functions. in NASCA23, Book of abstracts. https://hdl.handle.net/21.15107/rcub_machinery_6962
Tomanović J. Gauss-type quadrature rules for variable-sign weight functions. in NASCA23, Book of abstracts. 2023;. https://hdl.handle.net/21.15107/rcub_machinery_6962 .
Tomanović, Jelena, "Gauss-type quadrature rules for variable-sign weight functions" in NASCA23, Book of abstracts (2023), https://hdl.handle.net/21.15107/rcub_machinery_6962 .