Tikhonov regularization of large linear problems
type: Item
instance of: scholarly article
title: Tikhonov regularization of large linear problems
zbMATH Open document ID: 1038.65048
DOI: 10.1023/A:1026083619097
published in: BIT
publication date: 2003-12-04T00:00:00Z
review text: The authors present a new numerical method for computing regularized solutions of Tikhonov regularization applied to large scale discrete linear ill-posed problems. The method is based on Lanczos bidiagonalization and Gauss quadrature. For choosing the regularization parameter the discrepancy principle is used. In addition to some details concerning the numerical analysis of the approach a comprehensive case study for Fredholm integral equations is presented. The results are compared with those of fast conjugate-gradient-based methods for Tikhonov regularization introduced by \textit{A. Frommer} and \textit{P. Maass} [SIAM J. Sci. Comput. 20, 1831--1850 (1999; Zbl 0943.65068)]. The authors note that the new method is able to reduce the number of matrix-vector product evaluations.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65R30
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47A52
zbMATH DE Number: 2012826
zbMATH Keywords: Ill-posed problem
zbMATH Keywords: large scale problem
zbMATH Keywords: Lanczos bidiagonalization
zbMATH Keywords: Gauss quadrature
zbMATH Keywords: discrepancy principle
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: Fredholm integral equations
author: Daniela Calvetti
author: Lothar Reichel
reviewed by: Bernd Hofmann
MaRDI profile type: Publication
full work available at URL: a:1026083619097
OpenAlex ID: W64572908
description: scientific article; zbMATH DE number 2012826