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Numerical Solutions of Differential Equations for the Analytic Singular Value Decomposition

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. Previous approaches to this problem have used algebraic minimisation techniques and explicit Runge-Kutta solution of differential equations satisfied by the ASVD. Here the explicit method is reviewed and alternative methods based on implicit Gauss point collocation are considered. Special properties of this approach which make it particularly attractive are described, and the idea of stabilization of the equations is introduced. Examples are given which illustrate some of the alternatives implemented in fixed step mode.

Publication metadata

Author(s): Wright K

Publication type: Report

Publication status: Published

Series Title: Department of Computing Science Technical Report Series

Year: 1992

Pages: 18

Print publication date: 01/10/1992

Source Publication Date: October 1992

Report Number: 405

Institution: Department of Computing Science, University of Newcastle upon Tyne

Place Published: Newcastle upon Tyne

URL: http://www.cs.ncl.ac.uk/publications/trs/papers/405.pdf

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