Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight
type: Item
instance of: scholarly article
title: Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight
zbMATH Open document ID: 0856.65011
DOI: 10.1016/0377-0427(95)00232-4
author: B. D. Keister
author: A. Genz
published in: Journal of Computational and Applied Mathematics
publication date: 1997-02-24T00:00:00Z
review text: This paper deals with the construction of numerical methods for the estimation of integrals of the form \[ I(f) = {1\over(2\pi)^{n/2}} \int^\infty_{-\infty} \int^\infty_{-\infty} \cdots \int^\infty_{-\infty}e^{-x^Tx/2} f(x)dx_1,dx_2 \cdots dx_n \] with \(x=(x_1,x_2,\dots,x_n)^T\). Fully symmetric interpolatory integration rules are constructed for multidimensional integrals over infinite integration regions with a Gaussian weight function. The points for these rules are determined by successive extensions of the one-dimensional three-point Gauss-Hermite rule. The new rules are shown to be efficient and only moderately unstable.
reviewed by: R. S. Dahiya
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 910318
zbMATH Keywords: fully symmetric interpolatory integration rules
zbMATH Keywords: multidimensional integrals
zbMATH Keywords: infinite integration regions
zbMATH Keywords: Gaussian weight function
zbMATH Keywords: three-point Gauss-Hermite rule
describes a project that uses: PATSYM
describes a project that uses: FWTPTS
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00232-4
OpenAlex ID: W2109012275
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description: scientific article; zbMATH DE number 910318