K. Wright
University of Newcastle upon Tyne. 1992
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.