The analytic SVD: On the non-generic points on the path

Abstract

A new technique for computing the Analytic SVD is proposed. The idea is to follow a branch of just one simple singular value and the corresponding left/right singular vector. Numerical computation may collapse at non-generic points; we will consider the case when the continuation gets stuck due to a nonzero multiple singular value. We interpret such a point as a singularity of the branch. We employ singularity theory in order to describe and classify this point. Since its codimension is one, we meet such a point “rarely.”

Full Text (PDF) [309 KB], BibTeX

Key words

SVD, ASVD, continuation, singularity theory.

65F15

Links to the cited ETNA articles

 [12] Vol. 1 (1993), pp. 72-88 Volker Mehrmann and Werner Rath: Numerical methods for the computation of analytic singular value decompositions

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