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<p>Split quaternions, with their unique algebraic properties, pose challenges in numerical analysis, particularly due to the presence of zero divisors. While traditional tensor equations have been well-explored, split quaternion tensor equations remain relatively under-researched. This paper develops algorithms for solving the equation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {E}*_N\mathcal {X}*_N\mathcal {F}=\mathcal {D}\)</EquationSource> </InlineEquation>, and provide rigorous convergence analyses together with comprehensive evaluations of their computational complexity. Among these methods, we identify the three algorithms that demonstrate the best practical performance. Numerical experiments are provided for these algorithms, and their effectiveness is further illustrated through applications to color image encryption and decryption.</p>

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Iteration methods for the classical split quaternion tensor equation \(\mathcal {E}*_N\mathcal {X}*_N\mathcal {F}=\mathcal {D}\)

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • Zi-Han Gao,
  • Qing-Wen Wang

摘要

Split quaternions, with their unique algebraic properties, pose challenges in numerical analysis, particularly due to the presence of zero divisors. While traditional tensor equations have been well-explored, split quaternion tensor equations remain relatively under-researched. This paper develops algorithms for solving the equation \(\mathcal {E}*_N\mathcal {X}*_N\mathcal {F}=\mathcal {D}\) , and provide rigorous convergence analyses together with comprehensive evaluations of their computational complexity. Among these methods, we identify the three algorithms that demonstrate the best practical performance. Numerical experiments are provided for these algorithms, and their effectiveness is further illustrated through applications to color image encryption and decryption.