论文信息 - Singular value decomposition of time-varying matrices

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.

Uwe Helmke | Markus Baumann

[1] Timo Eirola,et al. On Smooth Decompositions of Matrices , 1999, SIAM J. Matrix Anal. Appl..

[2] Tosio Kato. Perturbation theory for linear operators , 1966 .

[3] K. Wright. Differential equations for the analytic singular value decomposition of a matrix , 1992 .

[4] R. Abraham,et al. Manifolds, Tensor Analysis, and Applications , 1983 .

[5] U. Helmke,et al. Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.

[6] R. Abraham,et al. Manifolds, tensor analysis, and applications: 2nd edition , 1988 .

[7] H. W. Braden,et al. The Equations ATX\pm XTA=B , 1999, SIAM J. Matrix Anal. Appl..

[8] J. Marsden,et al. Dynamic inversion of nonlinear maps with applications to nonlinear control and robotics , 1995 .

[9] Jerrold E. Marsden,et al. Dynamical methods for polar decomposition and inversion of matrices , 1997 .