Automatic stopping rule for iterative methods in discrete ill-posed problems
type: Item
instance of: scholarly article
title: Automatic stopping rule for iterative methods in discrete ill-posed problems
zbMATH Open document ID: 1337.65034
author: Leonardo Borges
author: Fermín S. V. Bazán
author: M. C. C. Cunha
published in: Computational and Applied Mathematics
publication date: 2015-10-23T00:00:00Z
review text: This paper deals with the underlying properties of a stopping rule for the least squares QR-methods proposed recently by \textit{F. S. V. Bazán} et al. [Numer. Linear Algebra Appl. 21, No. 3, 316--339 (2014; Zbl 1340.65071)], and shows how to extend it to Krylov subspace projection methods such as the generalized minimal residual method, the minimal residual method, etc., for which regularization is achieved by projecting the original problem onto a Krylov subspace and where the dimension of this subspace plays the role of the regularization parameter. The authors also consider how to apply the rule to certain preconditioned versions of these methods. Like the original rule, the extended version works well without requiring a priori knowledge about the error norm.
Mathematics Subject Classification ID: 65F22
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 6497596
zbMATH Keywords: ill-posed problem
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: parameter choice
zbMATH Keywords: preconditioning
zbMATH Keywords: stopping rule
zbMATH Keywords: projection method
zbMATH Keywords: regularization
zbMATH Keywords: least squares QR-methods
zbMATH Keywords: generalized minimal residual method
reviewed by: Liu Xinguo
describes a project that uses: corner.m
describes a project that uses: LSQR
describes a project that uses: Regularization tools
describes a project that uses: CRAIG
MaRDI profile type: Publication
full work available at URL: s40314-014-0174-3
OpenAlex ID: W2077994701
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DOI: 10.1007/S40314-014-0174-3
description: scientific article; zbMATH DE number 6497596