Perturbation theory for orthogonal projection methods with applications to least squares and total least squares
type: Item
instance of: scholarly article
title: Perturbation theory for orthogonal projection methods with applications to least squares and total least squares
zbMATH Open document ID: 0843.65027
DOI: 10.1016/0024-3795(94)00209-6
author: Ricardo D. Fierro
author: James R. Bunch
published in: Linear Algebra and its Applications
publication date: 1996-02-26T00:00:00Z
review text: The paper presents new perturbation theory for orthogonal projection methods with applications to least squares (LS) and total least squares (TLS). Current perturbation theory does not justify the superiority of TLS over LS. The authors derive new lower and upper perturbation bounds for orthogonal projection methods in terms of the subspace angle and the norms of the solutions. These bounds show that TLS is usually more robust than LS under perturbation of all the data. Furthermore, the new bounds permit a comparison between the LS and TLS solutions as well as between any two orthogonal projection methods. Numerical simulations show that the lower and upper bounds provide realistic estimates of the error. They illustrate that the TLS subspaces usually ``filter'' more noise that the LS subspaces.
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 847494
zbMATH Keywords: perturbation theory
zbMATH Keywords: orthogonal projection methods
zbMATH Keywords: least squares
zbMATH Keywords: total least squares
zbMATH Keywords: perturbation bounds
describes a project that uses: VanHuffel
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00209-6
OpenAlex ID: W2023054423
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description: scientific article; zbMATH DE number 847494