Convergence analysis of projected fixed-point iteration on a low-rank matrix manifold

D. A. Kolesnikov, I. V. Oseledets

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    2 Citations (Scopus)


    In this paper, we analyze the convergence of a projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method, we use the projector splitting scheme. We prove that the convergence rate of the projector splitting scheme is bounded by the convergence rate of standard fixed-point iteration without rank constraints multiplied by the function of initial approximation. We also provide counterexample to the case when conditions of the theorem do not hold. Finally, we support our theoretical results with numerical experiments.

    Original languageEnglish
    Article numbere2140
    JournalNumerical Linear Algebra with Applications
    Issue number5
    Publication statusPublished - Oct 2018


    • fixed-point iteration
    • low-rank approximation
    • Riemannian optimization framework


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