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2022 The Least Squares Solution with the Minimal Norm to a System of Mixed Generalized Sylvester Reduced Biquaternion Tensor Equations
Anli Wei, Ying Li, Shufang Yue, Jianli Zhao
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Taiwanese J. Math. Advance Publication 1-18 (2022). DOI: 10.11650/tjm/220901

Abstract

In this paper, we investigate the least squares solution with the minimal norm to the system (1.1) over reduced biquaternion via complex representation of reduced biquaternion tensors and the Moore–Penrose inverse of tensors. Besides, we establish some necessary and sufficient conditions for the solvability to the above system and give an expression of the general solution to the system when the solvability conditions are met. Moreover, the algorithm and numerical example are presented to verify the main results of this paper.

Funding Statement

This work was supported by the National Natural Science Foundation of China under grant 62176112, the Natural Science Foundation of Shandong Province under grant ZR2020MA053.

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Anli Wei. Ying Li. Shufang Yue. Jianli Zhao. "The Least Squares Solution with the Minimal Norm to a System of Mixed Generalized Sylvester Reduced Biquaternion Tensor Equations." Taiwanese J. Math. Advance Publication 1 - 18, 2022. https://doi.org/10.11650/tjm/220901

Information

Published: 2022
First available in Project Euclid: 12 September 2022

Digital Object Identifier: 10.11650/tjm/220901

Subjects:
Primary: ‎15A09 , 15A69

Keywords: complex representation , least squares solution , reduced biquaternion tensor , Sylvester tensor equations

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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