Volume 1, pp. 72-88, 1993.

Numerical methods for the computation of analytic singular value decompositions

Volker Mehrmann and Werner Rath

Abstract

An analytic singular value decomposition (ASVD) of a path of matrices $E(t)$ is an analytic path of factorizations $E(t)=X(t)S(t)Y(t{)}^T$ where $X(t)$ and $Y(t)$ are orthogonal and $S(t)$ is diagonal. The diagonal entries of $S(t)$ are allowed to be either positive or negative and to appear in any order. For an analytic path matrix $E(t)$ an ASVD exists, but this ASVD is not unique. We present two new numerical methods for the computation of unique ASVD's. One is based on a completely algebraic approach and the other on one step methods for ordinary differential equations in combination with projections into the set of orthogonal matrices.

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Key words

analytic singular value decomposition, singular value decomposition.

AMS subject classifications

65F25.

ETNA articles which cite this article

Vol. 37 (2010), pp. 70-86 Dáša Janovská and Vladimír Janovský: The analytic SVD: On the non-generic points on the path