Some solutions to a third-order quaternion tensor equation-Reference-Cited by-同舟云学术

Some solutions to a third-order quaternion tensor equation

Published:2023 Issue:11 Volume:8 Page:27725-27741
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Li Xiaohan¹²,Liu Xin³,Jiang Jing¹,Sun Jian²

Affiliation:

1. Department of Mathematics, QiLu Normal University, Jinan 250013, China

2. School of Computer Science and Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, Taipa 999078, China

3. Macau Institute of Systems Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Avenida Wai Long, Taipa 999078, China

Abstract

<abstract><p>The paper deals with the third-order quaternion tensor equation. Based on the Qt multiplication operation, we derive solvability conditions and also get the general solution, the least-squares solution, the minimum-norm solution and the minimum-norm least-squares solution of the tensor equation $ \mathcal{A} \ast_{\mathbb{Q}} \mathcal{X} = \mathcal{B} $. Finally, two numerical examples are presented.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference16 articles.

1. S. D. Leo, G. Scolarici, Right eigenvalue equation in quaternionic quantum mechanics, J. Phys. A Math. Gen., 33 (2000), 2971–2995. http://dx.doi.org/10.1088/0305-4470/33/15/306

2. N. L. Bihan, S. J. Sangwine, Quaternion principal component analysis of color images, In: Proceedings of the IEEE Conference on Image Processing (ICIP), 1 (2003), 903–908. http://dx.doi.org/10.1109/ICIP.2003.1247085

3. S. J. Sangwine, N. L. Bihan, Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations, Appl. Math. Comput., 182 (2006), 727–738. https://doi.org/10.1016/j.amc.2006.04.032

4. A. K. Smilde, P. Geladi, R. Bro, Multi-way Analysis: Applications in the Chemical Sciences, Hoboken: Wiley, 2005.

5. P. Soto-Quiros, A least-squares problem of a linear tensor equation of third-order for Audio and color image processing, In: 2022 45th International Conference on Telecommunications and Signal Processing, 2022, 59–65. https://doi.org/10.1109/TSP55681.2022.9851367