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Differential Equations for the Analytic Singular Value Decomposition of a Matrix

Lookup NU author(s): Dr Kenneth Wright

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Abstract

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 minimisation 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.

Publication metadata

Author(s): Wright K

Publication type: Article

Publication status: Published

Journal: Numerische Mathematik

Year: 1992

Volume: 63

Issue: 2

Pages: 283-295

Date deposited: 24/09/2010

ISSN (print): 0029-599X

ISSN (electronic): 0945-3245

Publisher: Springer

URL: http://dx.doi.org/10.1007/BF01385862

DOI: 10.1007/BF01385862

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