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<p>In this paper, we study an effective algorithm for the Schur decomposition of a quaternion matrix. Firstly, we give a complex structure-preserving algorithm for the Hessenberg decomposition of a quaternion matrix by Householder transformation. Secondly, we implement the implicit double shift QR strategy on the obtained Hessenberg matrix, and design the corresponding complex structure-preserving algorithm. Moreover, the effectiveness of the newly proposed algorithm is verified by numerical experiments. At last, the proposed algorithm is used to deal with a blind color image watermarking problem.</p>

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A New Complex Structure-Preserving Quaternion Implicit Double Shift QR Algorithm

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Jianhua Sun,
  • Ying Li,
  • Mingcui Zhang,
  • Musheng Wei

摘要

In this paper, we study an effective algorithm for the Schur decomposition of a quaternion matrix. Firstly, we give a complex structure-preserving algorithm for the Hessenberg decomposition of a quaternion matrix by Householder transformation. Secondly, we implement the implicit double shift QR strategy on the obtained Hessenberg matrix, and design the corresponding complex structure-preserving algorithm. Moreover, the effectiveness of the newly proposed algorithm is verified by numerical experiments. At last, the proposed algorithm is used to deal with a blind color image watermarking problem.