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Real and complex solutions of the total least squares problem in commutative quaternionic theory

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Abstract

As a very effective research tool, the commutative quaternion least squares (LS) problems, especially the commutative quaternion total least squares (TLS) problems, have a wide range of potential applications in mathematical physics, telecommunications, and image processing. This paper studies the commutative quaternion TLS problem using the real and complex representation of a commutative quaternion matrix and gives two algorithms for solving the real and complex solutions of the commutative quaternion TLS problem in commutative quaternionic theory.

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Authors and Affiliations

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

    Dong Zhang, Zhenwei Guo & 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. Dong Zhang
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  2. Tongsong Jiang
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  3. Zhenwei Guo
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  4. V. I. Vasil’ev
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Correspondence to Tongsong Jiang or V. I. Vasil’ev.

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The research of Tongsong Jiang and Zhenwei Guo is supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No. 075-02-2024-1441, February 28, 2024 (sections 2, 3). The research of V.I. Vasil’ev and Dong Zhang is supported by the Russian Science Foundation grant No. 23-71-30013 (sections 4, 5). The research of Dong Zhang and Zhenwei Guo is supported by the Chinese Government Scholarship (CSC No. 202108370086, CSC No. 202108370087).

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Zhang, D., Jiang, T., Guo, Z. et al. Real and complex solutions of the total least squares problem in commutative quaternionic theory. Comp. Appl. Math. 43, 235 (2024). https://doi.org/10.1007/s40314-024-02755-x

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  • DOI: https://doi.org/10.1007/s40314-024-02755-x

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