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<p>In this paper, we propose a quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving the quaternion matrix equation and prove that it converges to the unique least Frobenius norm solution. To accelerate the convergence, we incorporate the adaptive stochastic heavy ball momentum into the quaternion relaxed greedy randomized Kaczmarz method, and provide the corresponding convergence analysis framework. Numerical simulations are conducted to demonstrate the feasibility and effectiveness of the proposed methods, particularly in the color image restoration.</p>

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The quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving quaternion matrix equation

  • 期刊论文

  • 发表日期：

    2025年4月21日

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  • Xiaojian Ding,
  • Baohua Huang

摘要

In this paper, we propose a quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving the quaternion matrix equation and prove that it converges to the unique least Frobenius norm solution. To accelerate the convergence, we incorporate the adaptive stochastic heavy ball momentum into the quaternion relaxed greedy randomized Kaczmarz method, and provide the corresponding convergence analysis framework. Numerical simulations are conducted to demonstrate the feasibility and effectiveness of the proposed methods, particularly in the color image restoration.