Singular value decomposition of time-varying matrices

Authors:
Markus Baumann;Uwe Helmke
Affiliations:
Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany;Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
Venue:
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Year:
2003

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Abstract

This paper is concerned with an algorithm to compute the singular value decomposition (SVD) of time-varying square matrices. In a first step we consider the task of diagonalizing symmetric time-varying matrices A(t). A differential equation is proposed, whose solutions asymptotically track the diagonalizing transformation. In particular, perfect matching of the initial conditions is not required and the solutions converge exponentially towards the desired transformation. Then the desired differential equation for tracking the SVD is derived. Robustness of the algorithms is guaranteed by our approach.