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An efficient method for the total least squares problem in reduced biquaternionic electromagnetics

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Abstract

In the theoretical explorations and numerical computations in reduced biquaternionic electromagnetics, the reduced biquaternion total least squares (RBTLS) problem is an extremely effective tool for the study of reduced biquaternionic electromagnetics and electromagnetic field theory. This paper studies for the first time the RBTLS problem by means of a complex representation of a reduced biquaternion matrix, derives the necessary and sufficient conditions for the RBTLS problem to have a reduced biquaternion solution, and gives an efficient algorithm for solving the RBTLS problem. Finally, numerical examples are presented to demonstrate the efficiency of the proposed algorithm.

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Acknowledgements

The research of T. Jiang is supported by the Ministry of science and higher education of the Russian Federation, agreement (No. 075-02-2023-947, February 16, 2023). The work of V. I. Vasil’ev has been supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. FSRG-2023-0025). The research of D. Zhang and G. Wang is supported by the Russian Science Foundation grant (23-71-30013). The research of D. Zhang is supported by the Chinese Government Scholarship (CSC No. 202108370086). The research of G. Wang is supported by the Chinese Government Scholarship (CSC No. 202008370340).

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Authors and Affiliations

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

    Dong Zhang, Gang Wang & 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

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  1. Dong Zhang
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Correspondence to Tongsong Jiang.

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Zhang, D., Jiang, T., Wang, G. et al. An efficient method for the total least squares problem in reduced biquaternionic electromagnetics. Eur. Phys. J. Plus 138, 826 (2023). https://doi.org/10.1140/epjp/s13360-023-04419-x

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