https://doi.org/10.1140/epjp/s13360-023-04419-x
Regular Article
An efficient method for the total least squares problem in reduced biquaternionic electromagnetics
1
Institute of Mathematics and Information Science, North-Eastern Federal University, 677000, Yakutsk, Russia
2
School of Electronic Information, Shandong Xiandai University, 250104, Jinan, Shandong, People’s Republic of China
3
School of Mathematics and Statistics, Linyi University, 276005, Linyi, Shandong, People’s Republic of China
Received:
30
May
2023
Accepted:
28
August
2023
Published online:
21
September
2023
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
