Verified bounds for least squares problems and underdetermined linear systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 1255.65082
DOI: 10.1137/110840248
published in: SIAM Journal on Matrix Analysis and Applications
publication date: 2012-08-23T00:00:00Z
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65G20
zbMATH DE Number: 6070721
zbMATH Keywords: underdetermined linear system
zbMATH Keywords: normal equations
zbMATH Keywords: extra-precise residual evaluation
zbMATH Keywords: algorithm
zbMATH Keywords: verified error bounds
zbMATH Keywords: linear least squares problem
zbMATH Keywords: sparse problem
zbMATH Keywords: numerical experiments
author: Siegfried M. Rump
describes a project that uses: Matlab
describes a project that uses: SparseMatrix
describes a project that uses: XBLAS
describes a project that uses: INTLAB
MaRDI profile type: Publication
OpenAlex ID: W2158149279
title: Verified bounds for least squares problems and underdetermined linear systems
review text: Algorithms for computing verified error bounds for linear least squares problems and underdetermined linear systems are introduced. Compared to other approaches, they do not rely on normal equations and the results are applicable also for sparse problems. The decrease of the accuracy of the previously existing bounds is circumvented by using extra precision for residual evaluations and the efficiency (in terms of the accuracy and computing time) is reported in numerical experiments. The algorithms are implemented in the Matlab toolbox INTLAB.
reviewed by: Pavel Jiránek
description: scientific article; zbMATH DE number 6070721