Convergence analysis of a regularized approximation for solving Fredholm integral equations of the first kind
type: Item
instance of: scholarly article
title: Convergence analysis of a regularized approximation for solving Fredholm integral equations of the first kind
zbMATH Open document ID: 1021.65070
DOI: 10.1016/S0022-247X(03)00027-1
author: M. P. Rajan
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: The author discusses the convergence of numerical solutions of Fredholm integral equations of the first kind using Tikhonov regularization under surpremum norm. He considers the approximate equations \[ (A_n + \alpha I) \widetilde{x}_{\alpha, n}=F_n\widetilde{y} . \] and carries out the convergence analysis in the \(L^2\) norm . An a priori parameter choice strategy for choosing the regularization parameters and the error estimate are provided. The author also extends this work under a supremum norm setting.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65R30
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 1915767
zbMATH Keywords: ill-posed problems
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: supremum norm
zbMATH Keywords: Fredholm integral equations of the first kind
zbMATH Keywords: parameter choice strategy
zbMATH Keywords: error estimate
reviewed by: Zhang Wanguo
MaRDI profile type: Publication
cites work: Q3334886
cites work: Q3719776
cites work: Convergence analysis of a regularized degenerate kernel method for Fredholm integral equations of the first kind
cites work: A unified approach for regularised approximation methods for fredholm integralequations of the first kind equations of the first kind
cites work: A modified convergence analysis for solving Fredholm integral equations of the first kind
description: scientific article; zbMATH DE number 1915767