Title

A Modified Tikhonov Regularization For Linear Operator Equations

Keywords

Convergence and asymptotic order of the regularized solutions; Error analysis; First kind operator equation; Ill-posed problem; Modified Tikhonov regularization

Abstract

We construct with the aid of regularizing filters a new class of improved regularization methods, called modified Tikhonov regularization (MTR), for solving ill-posed linear operator equations. Regularizing properties and asymptotic order of the regularized solutions are analyzed in the presence of noisy data and perturbation error in the operator. With some accurate estimates in the solution errors, optimal convergence order of the regularized solutions is obtained by a priori choice of the regularization parameter. Furthermore, numerical results are given for several ill-posed integral equations, which not only roughly coincide with the theoretical results but also show that MTR can be more accurate than ordinary Tikhonov regularization (OTR). Copyright © Taylor & Francis, Inc.

Publication Date

11-17-2005

Publication Title

Numerical Functional Analysis and Optimization

Volume

26

Issue

4-5

Number of Pages

543-563

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/01630560500248389

Socpus ID

27744496675 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/27744496675

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