Orthogonal polynomials, random matrices and the numerical inversion of the Laplace transform of positive functions
type: Item
instance of: scholarly article
title: Orthogonal polynomials, random matrices and the numerical inversion of the Laplace transform of positive functions
zbMATH Open document ID: 1021.65068
DOI: 10.1016/S0377-0427(02)00871-3
author: Piero Barone
published in: Journal of Computational and Applied Mathematics
publication date: 2003-06-17T00:00:00Z
review text: A method for the numerical inversion of the Laplace transform of a continuous positive function \(f(t)\) is proposed. Random matrices distributed according to a Gibbs law whose energy \(V(x)\) is a function of \(f(t)\) are considered as well as random polynomials orthogonal w.r.t. \(w(x)= e^{-V(x)}\). The equation relating \(w(x)\) to the reproducing kernel and to the condensed density of the roots of the random orthogonal polynomials is exploited. The qualitative behavior of the solutions provided by the proposed method is illustrated by numerical examples and discussed by using logarithmic potentials with external fields that give insight into the asymptotic behavior of the condensed density when the number of the data points goes to infinity.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 65R30
Mathematics Subject Classification ID: 65R32
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 15B52
zbMATH DE Number: 1929358
zbMATH Keywords: random matrices
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: ill-posed inverse problems
zbMATH Keywords: logarithmic potentials
zbMATH Keywords: moment problems
zbMATH Keywords: Laplace transform
zbMATH Keywords: reproducing kernel
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1929358