A method of parametric solution of convolution equations
type: Item
instance of: scholarly article
title: A method of parametric solution of convolution equations
zbMATH Open document ID: 1405.65179
author: A. N. Ushakova
published in: Journal of Mathematical Sciences (New York)
publication date: 2018-04-05T00:00:00Z
review text: The paper considers the approximate numerical solution of a convolution-type integral equation \[ \int_{-\infty}^\infty K(t-s) z(s) \,ds = u(t), \] where \(K\) and \(u\) are known, and \(z(t)\) is an unknown function. It is assumed that \(z(t)\) belongs to a family of functions described by a small number of parameters. Of special interest are the gamma model \[ z(t;\alpha,\beta) = \frac{\beta^\alpha}{\Gamma(\alpha)} t^{\alpha-1} e^{-\beta t}, \] and the shifted gamma model \[ z(t;\alpha,\beta,\tau) = \frac{\beta^\alpha}{\Gamma(\alpha)} (t-\tau)^{\alpha-1} e^{-\beta (t-\tau)}. \] Relationships between the moments of \(K\), \(z\), and \(u\) lead to a system of equations for the parameters, which can then be solved numerically. The author points out that this approach can also be used in the Tikhonov regularization, by using the parametric solution to estimate the regularization parameter \(\delta\).
reviewed by: Fritz Keinert
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 6856163
zbMATH Keywords: Fredholm integral equation
zbMATH Keywords: first kind
zbMATH Keywords: regularization
MaRDI profile type: Publication
full work available at URL: s10958-017-3646-3
OpenAlex ID: W2776323394
cites work: Q3948517
cites work: Influence of delayed viral production on viral dynamics in HIV-1 infected patients
cites work: On the global stability of an SIRS epidemic model with distributed delays
cites work: Q4125663
DOI: 10.1007/S10958-017-3646-3
description: scientific article; zbMATH DE number 6856163