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<p>In this paper, we propose innovative iterative algorithms founded on the gradient method to address conjugate transpose matrix equations for both real and complex matrices. A comprehensive analysis of the convergence behavior of these methods is conducted, alongside the development of practical numerical techniques for obtaining solutions efficiently. One of these methods uses the momentum technique. In this method, the optimal parameter of momentum is also determined. To substantiate the efficacy of the proposed iterative methods, we present diverse numerical examples within this study and contrast the outcomes with those obtained using existing algorithms. Additionally, we apply these methods to discrete-time antilinear systems, demonstrating their effectiveness in real-world scenarios.</p>

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Solvability, exact solution and momentum acceleration gradient-based iterative algorithm for general matrix equation \( AXB+C\overline{X}D+EX^TF+GX^*H=J \) and studying its applications in discrete-time antilinear systems and color image restoration

  • 期刊论文

  • 发表日期：

    2025年6月6日

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  • Akbar Shirilord,
  • Mehdi Dehghan

摘要

In this paper, we propose innovative iterative algorithms founded on the gradient method to address conjugate transpose matrix equations for both real and complex matrices. A comprehensive analysis of the convergence behavior of these methods is conducted, alongside the development of practical numerical techniques for obtaining solutions efficiently. One of these methods uses the momentum technique. In this method, the optimal parameter of momentum is also determined. To substantiate the efficacy of the proposed iterative methods, we present diverse numerical examples within this study and contrast the outcomes with those obtained using existing algorithms. Additionally, we apply these methods to discrete-time antilinear systems, demonstrating their effectiveness in real-world scenarios.