Weighted quadrature formulas for semi-infinite range integrals
Weighted quadrature formulas on the half line \((a,+\infty)\), \(a>0\), for non-exponentially decreasing integrands are developed. Such \(n\)-point quadrature rules are exact for all functions of the form \(x\mapsto x^{-2}P(x^{-1})\), where \(P\) is an arbitrary algebraic polynomial of degree at...
| الحاوية / القاعدة: | Journal of Numerical Analysis and Approximation Theory |
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| المؤلف الرئيسي: | |
| التنسيق: | مقال |
| اللغة: | الإنجليزية |
| منشور في: |
Publishing House of the Romanian Academy
2015-12-01
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://ictp.acad.ro/jnaat/journal/article/view/1063 |
| الملخص: | Weighted quadrature formulas on the half line \((a,+\infty)\), \(a>0\), for non-exponentially decreasing integrands are developed. Such \(n\)-point quadrature rules are exact for all functions of the form \(x\mapsto x^{-2}P(x^{-1})\), where \(P\) is an arbitrary algebraic polynomial of degree at most \(2n-1\). In particular, quadrature formulas with respect to the weight function \(x\mapsto w(x)=x^\beta\log^m x\) (\(0\le \beta<1\), \(m\in \mathbb{N}_0\)) are considered and several numerical examples are included.
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| تدمد: | 2457-6794 2501-059X |