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

• ID: 2439, RIV: 10051711
• ISSN: 1068-9613, ISBN: not specified
• source: Electronic Transactions on Numerical Analysis
• keywords: SVD; ASVD; continuation; singularity theory
• authors: Dáša Janovská, Vladimír Janovský
• authors from KNM: Janovský Vladimír

Abstract

A new technique for computing 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 collaps at non-generic points: The particular case when the continuation get stuck due to a nonzero multiple singular value is considered. Such a point is interpreted as a singularity of the branch. The Singularity Theory is employed in order to describe and classify this point.