四元数矩阵方程AXA^(H)=B的特殊最小二乘解  

The Special Least Squares Solutions of Quaternion Matrix Equation AXA^(H)=B

作　　者：岳树芳 李莹[1] 赵建立[1] 王栋 YUE Shufang;LI Ying;ZHAO Jianli;WANG Dong(College of Mathematical Sciences,Liaocheng University,Liaocheng Shandong 252000,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252000

出　　处：《重庆师范大学学报（自然科学版）》2021年第6期91-96,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11801249);山东省自然科学基金(No.ZR2020MA053)。

摘　　要：【目的】研究四元数矩阵方程AXA^(H)=B的最小二乘问题。【方法】提出四元数矩阵的一种新的实向量表示方法,结合矩阵的半张量积将四元数矩阵方程转换为相应实矩阵方程。【结果】给出该方程的最小二乘Hermitian(反Hermitian)三对角解,并得到有解的充要条件。【结论】通过数值算法与算例验证了该方法和结果的有效性。[Purposes]It mainly studies the least square solutions of quaternion matrix equation AXA^(H)=B.[Methods]A new kind of real representation of quaternion matrix is proposed.The quaternion matrix equation is transformed into the corresponding real matrix equation by combining the semi-tensor product of matrices.[Findings]The least squares Hermitian(anti-Hermitian)tridiagonal solutions of the equation are given,and the necessary and sufficient conditions for the existence of solutions are obtained.[Conclusions]The effectiveness of the method and results is demonstrated by numerical algorithm and example.

关 键 词：四元数矩阵方程 矩阵的半张量积 Hermitian三对角矩阵 反Hermitian三对角矩阵 

分 类 号：O241.6[理学—计算数学]