Extension of an error analysis of the randomized Kaczmarz method for inconsistent linear systems

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Author(s)

    • Morijiri Yushi
    • Graduate School of Information Science and Technology, The University of Tokyo
    • Aishima Kensuke
    • Graduate School of Information Science and Technology, The University of Tokyo
    • Matsuo Takayasu
    • Graduate School of Information Science and Technology, The University of Tokyo

Abstract

<p>In 2015, Gower and Richtárik presented a unifying framework for a variety of randomized iterative algorithms for consistent linear systems. The framework includes the randomized Kaczmarz method that exponentially converges in the mean square whenever the system is consistent. For noisy linear systems corresponding to inconsistent systems, the randomized Kaczmarz method computes an approximate solution within a fixed distance depending on the norm of the noise vector. We extend this error analysis to a general framework in inconsistent systems in a similar manner to Gower and Richtárik, and verify this theoretical analysis in numerical experiments. </p>

Journal

  • JSIAM Letters

    JSIAM Letters 10(0), 17-20, 2018

    The Japan Society for Industrial and Applied Mathematics

Codes

  • NII Article ID (NAID)
    130007404199
  • Text Lang
    ENG
  • ISSN
    1883-0609
  • Data Source
    J-STAGE 
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