Backward errors for eigenvalue and singular value decompositions
type: Item
instance of: scholarly article
title: Backward errors for eigenvalue and singular value decompositions
zbMATH Open document ID: 0807.65034
published in: Numerische Mathematik
publication date: 1995-02-28T00:00:00Z
review text: Bounds on the backward errors for the symmetric eigenvalue decomposition and the singular value decomposition in the two-norm and in the Frobenius norm are presented. When the computed eigenvectors have a small residual and are close to orthonormal then all backward errors tend to be small. Hence it does not matter how exactly a backward error is defined and how exactly residual and deviation from orthogonality are measured. The effects of the error bounds on implementation for eigenvectors and singular vectors are indicated. Finally, it is shown that the distance of an appropriately scaled matrix to its orthogonal QR factor is not much larger than its distance to the closest orthogonal matrix.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 691537
zbMATH Keywords: backward error bounds
zbMATH Keywords: symmetric eigenvalue decomposition
zbMATH Keywords: singular value decomposition
zbMATH Keywords: eigenvectors
zbMATH Keywords: singular vectors
author: S. Chandrasekaran
author: Ilse C. F. Ipsen
reviewed by: Wilhelm Heinrichs
MaRDI profile type: Publication
full work available at URL: s002110050057
OpenAlex ID: W1981814047
DOI: 10.1007/S002110050057
description: scientific article; zbMATH DE number 691537