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An algorithm based on QSVD for the quaternion equality constrained least squares problem

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Abstract

Quaternion equality constrained least squares (QLSE) problems have attracted extensive attention in the field of mathematical physics due to its applicability as an extremely effective tool. However, the knowledge gap among numerous QLSE problems has not been settled now. In this paper, by using quaternion SVD (Q-SVD) and the equivalence of the QLSE problem and Karush-Kuhb-Tucker (KKT) equation, we obtain some equations about the matrices in the general solution of the QLSE problem. Using these equations, an equivalent form of the solution of the QLSE problem is obtained. Then, applying the special structure of real representation of quaternion, we propose a real structure-preserving algorithm based on Q-SVD. At last, we give numerical example, which illustrates the effectiveness of our algorithm.

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Funding

This paper is supported by the Science Foundation of Liaocheng University under grants 31805 and 318011318.

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Authors and Affiliations

  1. School of Mathematical Science, Liaocheng University, Liaocheng, 252000, Shandong, People’s Republic of China

    Yanzhen Zhang, Ying Li & Musheng Wei

  2. School of Physics Science and Information Engineering, Liaocheng University, Liaocheng, 252000, Shandong, People’s Republic of China

    Hong Zhao

Authors
  1. Yanzhen Zhang
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  2. Ying Li
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  3. Musheng Wei
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  4. Hong Zhao
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Correspondence to Ying Li.

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Zhang, Y., Li, Y., Wei, M. et al. An algorithm based on QSVD for the quaternion equality constrained least squares problem. Numer Algor 87, 1563–1576 (2021). https://doi.org/10.1007/s11075-020-01019-z

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  • DOI: https://doi.org/10.1007/s11075-020-01019-z

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