An implicit shift bidiagonalization algorithm for ill-posed systems
type: Item
instance of: scholarly article
title: An implicit shift bidiagonalization algorithm for ill-posed systems
zbMATH Open document ID: 0821.65023
DOI: 10.1007/BF01934265
author: E. Grimme
author: Åke Björck
author: Paul van Dooren
published in: BIT
publication date: 1995-09-27T00:00:00Z
review text: Iterative methods based on Lanczos bidiagonalization (LBD) with full reorthogonalization are considered for solving large scale discrete ill- posed linear least squares problems of the form \(\min_ x \| Ax - b \|_ 2\). Section 1 discusses the use of generalized cross-validation to estimate the optimal regularization of an LBD solution when the noise level is unknown. Section 4 studies the implicitly restarted LBD method. Section 5 explores the use of implicit restarts in the context of determining regularization parameters for the LBD, and presents some numerical examples to demonstrate their efficiency.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 739435
zbMATH Keywords: ill-posed problem
zbMATH Keywords: Lanczos algorithm
zbMATH Keywords: iterative methods
zbMATH Keywords: Lanczos bidiagonalization with full reorthogonalization
zbMATH Keywords: large scale discrete ill-posed linear least squares problems
zbMATH Keywords: generalized cross-validation
zbMATH Keywords: implicit restarts
zbMATH Keywords: regularization parameters
zbMATH Keywords: numerical examples
reviewed by: Shenquan Xie
describes a project that uses: LSQR
describes a project that uses: eigs
describes a project that uses: CRAIG
describes a project that uses: Regularization tools
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01934265
OpenAlex ID: W1977271024
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description: scientific article; zbMATH DE number 739435