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Numerical Solution of Differential Equations for the Analytic Singular Value Decomposition
Lookup NU author(s)
Dr Kenneth Wright
Bainov, D., Covachev, V.
Conference Proceedings (inc. Abstract)
1st International Colloquium on Numerical Analysis
Year of Conference
13-17 August 1992
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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 minimization 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.
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