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Jacobi method for dual quaternion Hermitian eigenvalue problems and applications

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Abstract

Eigenvalue decomposition of quaternion Hermitian matrices is a crucial mathematical tool for color image reconstruction and recognition. Quaternion Jacobi method is one of the classical methods to compute the eigenvalues of a quaternion Hermitian matrix. Using quaternion Jacobi rotations, this paper brings forward an innovative method for the eigenvalue decomposition of dual quaternion Hermitian matrices. The effectiveness of the proposed method is confirmed through numerical experiments. Furthermore, a dual complex matrix representation for the color image is developed, and the dual quaternion Jacobi method is applied to the eigenvalue problems of dual complex Hermitian matrices. This approach achieves successful results in the color images reconstruction and recognition. Compared to the quaternion matrix representation of the color image, this approach makes computations more convenient when dealing with problems related to color image processing.

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Funding

This work is supported by the National Natural Science Foundation of China (62176112) and the Natural Science Foundation of Shandong Province (ZR2022MA030) and Discipline with Strong Characteristic of Liaocheng University Intelligent Science and Technology (319462208).

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515821, Guangdong, China

    Wenxv Ding

  2. College of Mathematics and Science, Liaocheng University, Liaocheng, 252000, Shandong, China

    Ying Li

  3. College of Mathematics and Science, Shanghai Normal University, Shanghai, 200234, China

    Musheng Wei

Authors
  1. Wenxv Ding
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  2. Ying Li
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  3. Musheng Wei
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Both authors contributed equally to this work.

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Correspondence to Ying Li.

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Ding, W., Li, Y. & Wei, M. Jacobi method for dual quaternion Hermitian eigenvalue problems and applications. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02112-5

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  • DOI: https://doi.org/10.1007/s12190-024-02112-5

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