On the solution of the finite moment problem
type: Item
instance of: scholarly article
title: On the solution of the finite moment problem
zbMATH Open document ID: 0765.65120
DOI: 10.1016/0022-247X(92)90346-F
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-04-01T00:00:00Z
review text: Let us consider the following first-kind integral equation with discrete data (1) \(Af=m\), \((Af)_ i:=\int_{-1}^ 1 x^{i-1} f(x)dx\), \(i=1,\dots,n\), where \(m:=(m_ 1,\dots,m_ n)\) is the known vector of moments and \(f\) is an unknown function. The authors give a method to obtain the normal solution of the equation (1) by a linear combination of Jacobi polynomials and obtain its coefficients in terms of the moments. Using ``MATLAB-386 Version 3.5e'' the authors show a number of examples to illustrate the method.
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 44A60
zbMATH DE Number: 150695
zbMATH Keywords: finite moment problem
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: numerical examples
zbMATH Keywords: first- kind integral equation
zbMATH Keywords: normal solution
zbMATH Keywords: Jacobi polynomials
author: G. Rodriguez
author: Sebastiano Seatzu
describes a project that uses: Matlab
MaRDI profile type: Publication
cites work: Hausdorff's moment problem and expansions in Legendre polynomials
cites work: Q5524836
cites work: Q5583224
cites work: Numerical solution of the finite moment problem in a reproducing kernel Hilbert space
cites work: Remarks concerning a numerical inversion of the Laplace transform due to Bellman, Kalaba, and Lockett
cites work: Q5620934
full work available at URL: 0022-247x(92)90346-f
OpenAlex ID: W2033175032
description: scientific article; zbMATH DE number 150695