40 Years of Computing at Newcastle

Department Technical Report Series No. 405

Numerical Solutions of Differential Equations for the Analytic Singular Value Decomposition

K. Wright

University of Newcastle upon Tyne. 1992

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 stabilisation of the equations is introduced. Examples are given which illustrate some of the alternatives implemented.


Department Technical Report Series - 1992
Department Technical Report Series Index
Contents Page - 40 Years of Computing at Newcastle
Technical Report Abstract No. 405, 27 June 1997