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Special least squares solutions of the reduced biquaternion matrix equation \(AX=B\) with applications

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Abstract

In this paper, using the real representation method, we study the reduced biquaternion matrix equation \(AX = B\). Taking advantage of the special structure of real representation of reduced biquaternion, we transform the problem of reduced biquaternion matrix into corresponding problem of real matrix. We propose the expressions of the special minimal norm least squares solution of the reduced biquaternion matrix equation \(AX = B\), and the corresponding algorithms only perform real arithmetic. Numerical examples are provided to illustrate that our algorithm are efficient and easily understood. We also apply the minimal norm pure imaginary least squares reduced biquaternion solution to color image restoration.

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Authors and Affiliations

  1. College of Mathematical Sciences, Liaocheng University, Liaocheng, 252000, People’s Republic of China

    Wenxv Ding, Ying Li & Dong Wang

  2. Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng, 252000, People’s Republic of China

    Wenxv Ding, Ying Li & Dong Wang

Authors
  1. Wenxv Ding
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  2. Ying Li
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  3. Dong Wang
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Correspondence to Ying Li.

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Communicated by Zhong-Zhi Bai.

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Supported by Science and Technology Project of Department of Education, Shandong Province ZR2020MA053, the science foundation of Liaocheng University under Grants 318011921.

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Ding, W., Li, Y. & Wang, D. Special least squares solutions of the reduced biquaternion matrix equation \(AX=B\) with applications. Comp. Appl. Math. 40, 279 (2021). https://doi.org/10.1007/s40314-021-01641-0

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  • DOI: https://doi.org/10.1007/s40314-021-01641-0

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