Singular value decomposition of time-varying matrices

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. (C) 2002 Elsevier Science B.V. All rights reserved.