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
Copyright Status
Unknown
Socpus ID
27744496675 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/27744496675
STARS Citation
Gongsheng, Li and Nashed, Zuhair, "A Modified Tikhonov Regularization For Linear Operator Equations" (2005). Scopus Export 2000s. 3540.
https://stars.library.ucf.edu/scopus2000/3540