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An efficient method for the split quaternion equality constrained least squares problem in split quaternionic mechanics

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Abstract

In the theoretical explorations and numerical computations of split quaternionic mechanics, a common and extremely effective tool for the study of quantum mechanics and quantum field theory is the split quaternion equality constrained least squares (LSESQ) problem. This paper for the first time studies the generalized singular value decomposition of split quaternion matrices (GSVDSQ) based on the \(2\times 2\) isomorphic representation of split quaternion matrices and obtains a GSVDSQ theorem. In addition, this paper proves the necessary and sufficient conditions for the LSESQ problem to have solutions and gives an efficient method for solving the LSESQ problem. Finally, two numerical examples are presented to demonstrate the efficiency of the proposed method.

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Authors and Affiliations

  1. Institute of Mathematics and Information Science, North-Eastern Federal University, Yakutsk, Russia, 677000

    Gang Wang, Dong Zhang & V. I. Vasil’ev

  2. School of Electronic Information, Shandong Xiandai University, Jinan, 250104, Shandong, People’s Republic of China

    Tongsong Jiang

  3. School of Mathematics and Statistics, Linyi University, Linyi, 276005, Shandong, People’s Republic of China

    Tongsong Jiang

Authors
  1. Gang Wang
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  2. Tongsong Jiang
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  3. Dong Zhang
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  4. V. I. Vasil’ev
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Corresponding authors

Correspondence to Tongsong Jiang or V. I. Vasil’ev.

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Communicated by Jinyun Yuan.

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The research of T. Jiang is supported by the Shandong Natural Science Foundation. The research of V. I. Vasil’ev, G. Wang and D. Zhang is supported by the Russian Science Foundation grant (23-71-30013). The research of G. Wang is supported by the Chinese Government Scholarship (CSC No. 202008370340). The research of D. Zhang is supported by the Chinese Government Scholarship (CSC No. 202108370086).

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Wang, G., Jiang, T., Zhang, D. et al. An efficient method for the split quaternion equality constrained least squares problem in split quaternionic mechanics. Comp. Appl. Math. 42, 258 (2023). https://doi.org/10.1007/s40314-023-02377-9

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  • DOI: https://doi.org/10.1007/s40314-023-02377-9

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