## 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.

Full Text (PDF) [239 KB]

### Key words

analytic singular value decomposition, singular value decomposition.

65F25.