Desingularization of bounded-rank matrix sets

Valentin Khrulkov, Ivan Oseledets

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    The conventional ways to solve optimization problems on low-rank matrix sets which appear in a great number of applications tend to ignore its underlying structure of an algebraic variety and existence of singular points. This leads to the appearance of inverses of singular values in algorithms and since they could be close to 0 it causes certain problems. We tackle this problem by utilizing ideas from algebraic geometry and show how to desingularize these sets. Our main result is an algorithm which uses only bounded functions of singular values and hence does not suffer from the issue described above.

    Original languageEnglish
    Pages (from-to)451-471
    Number of pages21
    JournalSIAM Journal on Matrix Analysis and Applications
    Volume39
    Issue number1
    DOIs
    Publication statusPublished - 2018

    Keywords

    • Algebraic geometry
    • Low-rankmatrices
    • Matrix completion
    • Riemannian optimization

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