求解四元数线性系统的一种新方法

doi:10.6040/j.issn.1671-9352.0.2022.013

Abstract

Abstract: The circulant solution of quaternion Stein equation is solved by using semi-tensor product of matrices and H-representation method. First, some new conclusions about the semi-tensor product of quaternion matrices are presented. The quaternion Stein equation is transformed into a matrix equation with independent variables by using this conclusions. Then, the sufficient and necessary conditions for the existence of the circulant solution and the general solution expression of the original system are given by using H-representation of the circulant matrix and classical matrix theory. Finally, the effectiveness of the algorithm is verified by the corresponding numerical algorithm, and the method is applied to solve quaternion Stein equations in linear time-varying systems.

Key words: quaternion Stein equation, semi-tensor product of matrices, H-representation, circulant matrix

CLC Number:

O241.6

FAN Xue-ling, LI Ying, ZHAO Jian-li, LIU Zhi-hong. A new method for solving quaternion linear system[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 55-64.

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A new method for solving quaternion linear system

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