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<p>The random reshuffling Kaczmarz (RRK) method enjoys the simplicity and efficiency in solving linear systems as a Kaczmarz-type method, whereas it also inherits the practical improvements of the stochastic gradient descent (SGD) with random reshuffling over original SGD. However, the current studies on RRK do not characterize its convergence comprehensively. In this paper, we present a novel analysis of the RRK method and prove its linear convergence toward the unique least-norm solution of the linear system. Furthermore, the convergence upper bound is tight and does not depend on the dimension of the coefficient matrix.</p>

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A Simple Linear Convergence Analysis of the Randomized Reshuffling Kaczmarz Method

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • De-Ren Han,
  • Jia-Xin Xie

摘要

The random reshuffling Kaczmarz (RRK) method enjoys the simplicity and efficiency in solving linear systems as a Kaczmarz-type method, whereas it also inherits the practical improvements of the stochastic gradient descent (SGD) with random reshuffling over original SGD. However, the current studies on RRK do not characterize its convergence comprehensively. In this paper, we present a novel analysis of the RRK method and prove its linear convergence toward the unique least-norm solution of the linear system. Furthermore, the convergence upper bound is tight and does not depend on the dimension of the coefficient matrix.