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<p>The Randomized Kaczmarz with Mismatched Adjoint (RKMA) method is an algorithm that resolves the imprecision adjoint matrix of linear systems by using sequential updates, avoiding the utilization of parallel computation. In this study, we explore a parallel version of RKMA, which implements an independently updated weighted average. We analyze the convergence of RKMA under both overdetermined and underdetermined systems using the averaging method. Additionally, we empirically showcase its performance, revealing that the convergence rate escalates with the increase in the number of threads, while the convergence level for inconsistent systems decreases.</p>

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Mismatched Adjoint Random Kaczmarz with Averaging

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Chen Guo,
  • Wei Huang

摘要

The Randomized Kaczmarz with Mismatched Adjoint (RKMA) method is an algorithm that resolves the imprecision adjoint matrix of linear systems by using sequential updates, avoiding the utilization of parallel computation. In this study, we explore a parallel version of RKMA, which implements an independently updated weighted average. We analyze the convergence of RKMA under both overdetermined and underdetermined systems using the averaging method. Additionally, we empirically showcase its performance, revealing that the convergence rate escalates with the increase in the number of threads, while the convergence level for inconsistent systems decreases.