Convergence acceleration of the Gauss-Laguerre quadrature formula
type: Item
instance of: scholarly article
title: Convergence acceleration of the Gauss-Laguerre quadrature formula
zbMATH Open document ID: 0929.65008
DOI: 10.1016/S0168-9274(98)00075-0
author: M. Kzaz
published in: Applied Numerical Mathematics
publication date: 2000-01-11T00:00:00Z
review text: The author studies the approximation of integrals of the form \(\int_0^\infty x^\alpha e^{-x}f(x) dx\) for \(\alpha \geq 0\) by the Gauss-Laguerre quadrature formula. Assuming that \(f\) is analytic in \((0,\infty)\) with a singularity at 0 and an asymptotic expansion in terms of \(e^z z^\beta z^{\alpha_j}(\log z)^{\beta _j}\) as \(\text{ Re} z \rightarrow \infty\) with \(\beta >-1\), an asymptotic expansion of the error term of the quadrature formula is derived. Based on this expansion, extrapolation schemes can be applied to improve the numerical approximations to the integral. This is illustrated at four examples.
reviewed by: Rudolf Wegmann
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 65B05
zbMATH DE Number: 1311295
zbMATH Keywords: convergence acceleration
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: numerical examples
zbMATH Keywords: Gauss-Laguerre quadrature formula
zbMATH Keywords: extrapolation schemes
MaRDI profile type: Publication
cites work: Extrapolation methods theory and practice
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description: scientific article; zbMATH DE number 1311295