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A real unconstrained equivalent problem of the quaternion equality constrained weighted least squares problem

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Abstract

In this paper, we focus on the quaternion equality constrained weighted least squares problem. First, according to the properties of the Moore-Penrose generalized inverse matrix, the singular value decomposition, the CS decomposition, and the real representation matrices of quaternion matrices, we obtain a real unconstrained equivalent problem of the quaternion equality constrained weighted least squares problem. And then we give the expressions of its general solution and minimal norm solution. Finally, according to the properties of the real representation matrices of quaternion matrices, the special structure of real representation matrices and the real structure-preserving singular value decomposition of quaternion matrix, we propose a real structure-preserving algorithm for the minimal norm solution of the quaternion equality constrained weighted least squares problem, and illustrate the effectiveness of proposed algorithm by a numerical example.

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Algorithm 1
Fig. 1
Fig. 2

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Data Availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Funding

This paper is supported by the Natural Science Foundation of Shandong Province of China (Nos. ZR2022MA030 and ZR2020MA053), the Scientific Research Foundation of Liaocheng University (No. 318011921), and Discipline with Strong Characteristics of Liaocheng University - Intelligent Science and Technology (No. 319462208).

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Authors and Affiliations

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

    Fengxia Zhang, Ying Li & Jianli Zhao

Authors
  1. Fengxia Zhang
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  2. Ying Li
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  3. Jianli Zhao
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Contributions

Fengxia Zhang wrote the main manuscript text and Ying Li prepared Figures 1–2. All authors reviewed the manuscript.

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Correspondence to Fengxia Zhang.

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Zhang, F., Li, Y. & Zhao, J. A real unconstrained equivalent problem of the quaternion equality constrained weighted least squares problem. Numer Algor 94, 73–91 (2023). https://doi.org/10.1007/s11075-022-01493-7

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  • DOI: https://doi.org/10.1007/s11075-022-01493-7

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