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<p>This paper investigates the existence and computation of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>(-anti)-Hermitian solutions for Sylvester quaternion matrix equations. By employing conjugate linear operator theory in quaternion algebra, we develop a novel quaternion modified conjugate gradient algorithm aimed at finding special solutions to matrix equations. The convergence characteristics of the newly proposed numerical approach are meticulously examined. Additionally, numerical experiments illustrate that the algorithm exhibits excellent practical performance and robust numerical stability.</p>

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Quaternion modified conjugate gradient algorithm for \(\eta \)(-anti)-Hermitian solutions of generalized coupled Sylvester-type quaternion matrix equations

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Xiaomin Cai,
  • Wenxin Zhuo,
  • Yifen Ke,
  • Riwei Liao

摘要

This paper investigates the existence and computation of \(\eta \) η (-anti)-Hermitian solutions for Sylvester quaternion matrix equations. By employing conjugate linear operator theory in quaternion algebra, we develop a novel quaternion modified conjugate gradient algorithm aimed at finding special solutions to matrix equations. The convergence characteristics of the newly proposed numerical approach are meticulously examined. Additionally, numerical experiments illustrate that the algorithm exhibits excellent practical performance and robust numerical stability.