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<p>Quaternion matrix equations play a very important role in control and system theory. In this paper, we consider the quaternion matrix equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{A}\textbf{X} = \textbf{B}\)</EquationSource> </InlineEquation> and propose a quaternion nonlinear conjugate gradient (QNCG) method. The convergence of the QNCG method is analyzed theoretically. The experimental results show that the QNCG method exhibits good performance in terms of computational efficiency and numerical stability, thereby verifying the feasibility and robustness of the method. In addition, the QNCG method is applied to the encryption and decryption of color image, demonstrating its practical application value.</p>

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A nonlinear conjugate gradient method for solving quaternion matrix equation and its application in color image encryption and decryption

  • 期刊论文

  • 发表日期：

    2026年1月15日

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  • Yuegui Zheng,
  • Baohua Huang

摘要

Quaternion matrix equations play a very important role in control and system theory. In this paper, we consider the quaternion matrix equation \(\textbf{A}\textbf{X} = \textbf{B}\) and propose a quaternion nonlinear conjugate gradient (QNCG) method. The convergence of the QNCG method is analyzed theoretically. The experimental results show that the QNCG method exhibits good performance in terms of computational efficiency and numerical stability, thereby verifying the feasibility and robustness of the method. In addition, the QNCG method is applied to the encryption and decryption of color image, demonstrating its practical application value.