Estimation of optimal backward perturbation bounds for the linear least squares problem
type: Item
instance of: scholarly article
title: Estimation of optimal backward perturbation bounds for the linear least squares problem
zbMATH Open document ID: 0905.65051
DOI: 10.1007/BF02510356
author: Rune Karlson
author: Bertil Waldén
published in: BIT
publication date: 1999-02-02T00:00:00Z
review text: Let \(\mathbb{R}^{m \times n}\) denote the set of real \(n\times n\) matrices, \(A\in \mathbb{R}^{m \times n}\), \(b\in \mathbb{R}^m\) and let \(\widetilde x\) be a purported solution to the minimization problem \(\min\| b-Ax \|_2\). The problem is to find a perturbation \(E\) of \(A\) such that \(\widetilde x\) minimizes \(\| b-(A+E) x\|_2\). The authors suggest a method for obtaining approximate estimates of the optimal backward perturbation bound, where the number of operations is moderate \((O(mn))\) in comparison with the work required to solve the least squares problem using standard techniques and therefore it is very suitable for large problems. The methods is based on the computation of a strict lower bound for the spectral norm and a strict upper bound for the Frobenius norm. Some results of computational experiments showing the efficiency of the proposed method are given.
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1117812
zbMATH Keywords: linear least squares problems
zbMATH Keywords: numerical examples
zbMATH Keywords: optimal backward perturbation bound
zbMATH Keywords: spectral norm
zbMATH Keywords: Frobenius norm
reviewed by: Otu Vaarmann
describes a project that uses: mctoolbox
MaRDI profile type: Publication
cites work: Q3359644
cites work: Q4864704
cites work: Optimal backward perturbation bounds for the linear least-squares problem with multiple right-hand sides
cites work: Optimal Backward Perturbation Bounds for Underdetermined Systems
cites work: Optimal backward perturbation bounds for the linear least squares problem
description: scientific article; zbMATH DE number 1117812