Differential equations for the analytic singular value decomposition of a matrix
type: Item
instance of: scholarly article
title: Differential equations for the analytic singular value decomposition of a matrix
zbMATH Open document ID: 0756.65060
DOI: 10.1007/BF01385862
author: S. Singh
published in: Numerische Mathematik
publication date: 1993-02-02T00:00:00Z
full work available at URL: https://eudml.org/doc/133682
review text: This paper is concerned with finding a smooth singular value decomposition for a matrix which is smoothly dependent on a parameter. A previous approach to this problem was based on minimization techniques, here, in contrast, a system of ordinary differential equations is derived for the decomposition. It is shown that the numerical solution of an initial value problem associated with these differential equations provides a feasible approach to the solution of this problem. Particular consideration is given to the situation which arises with equal modulus singular values which lead to indeterminacies in the evaluations needed for the numerical solution. Examples which illustrate the behaviour of the method are included.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A54
zbMATH DE Number: 86126
zbMATH Keywords: analytic singular value decomposition
zbMATH Keywords: parameter dependent matrix
zbMATH Keywords: smooth singular value decomposition
zbMATH Keywords: system of ordinary differential equations
MaRDI profile type: Publication
cites work: Numerical computation of an analytic singular value decomposition of a matrix valued function
cites work: Q4110164
description: scientific article; zbMATH DE number 86126