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<p>A surrogate hyperplane sparse extended Kaczmarz method which projects each iteration onto a surrogate hyperplane is proposed for computing sparse solutions of inconsistent linear systems. Three implementations for generating the surrogate hyperplane including the identity matrix columns, the residual and partial residual information obtained during the iteration are introduced. The convergence theories are established and their contraction factors are studied in details. Numerical experiments further verify the effectiveness of the proposed method in solving sparse least squares problems and image deblurring.</p>

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Extended sparse Kaczmarz method with surrogate hyperplane for sparse solutions to inconsistent linear systems

  • 期刊论文

  • 发表日期：

    2025年12月23日

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  • Ze Wang,
  • Yu-Xin Ye,
  • Jun-Feng Yin,
  • Shao-Liang Zhang

摘要

A surrogate hyperplane sparse extended Kaczmarz method which projects each iteration onto a surrogate hyperplane is proposed for computing sparse solutions of inconsistent linear systems. Three implementations for generating the surrogate hyperplane including the identity matrix columns, the residual and partial residual information obtained during the iteration are introduced. The convergence theories are established and their contraction factors are studied in details. Numerical experiments further verify the effectiveness of the proposed method in solving sparse least squares problems and image deblurring.