Rao coefficients for the solution of convolution integral equations
type: Item
instance of: scholarly article
title: Rao coefficients for the solution of convolution integral equations
zbMATH Open document ID: 0962.65116
DOI: 10.1016/S0010-4655(99)00522-6
author: S. O. Kastner
published in: Computer Physics Communications
publication date: 2001-05-31T00:00:00Z
review text: For the solution \(h(x)\) of the convolution integral equation \(f = h\ast g,\) given the kernel function \(g(x)\) and the convolution function \(f(x),\) \textit{J.~S.~Rao} [Proc. Indian Acad. Sci., Sect. A 65, 233-239 (1967; Zbl 0147.10602)] derived a useful expression \(h(x) =\sum_n a_nf^{(n)}(x)\) in terms of recursively defined coefficients \(a_n.\) In this paper, these coefficients are explicitly evaluated up to order \(n = 20\) in terms of moments of \(g(x).\) The software Maple is used to produce general expressions for the higher even order Rao coefficients, and numerical values of \(a_n\) for two forms of the Gaussian distribution.
reviewed by: Nikolay Yakovlevich Tikhonenko
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 1485016
zbMATH Keywords: convolution integral equation
zbMATH Keywords: deconvolution
zbMATH Keywords: inversion
zbMATH Keywords: Rao coefficients
zbMATH Keywords: Gaussian distribution
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: s0010-4655(99)00522-6
OpenAlex ID: W2079483620
Wikidata QID: Q126557262
description: scientific article; zbMATH DE number 1485016