Sylvester四元数矩阵方程Hankel解的半张量积方法  

Semi-tensor Product Method for Solving Least Square Hankel Solutions of Sylvester Quaternion Matrix Equation

作　　者：闫立梅[1] 赵琳琳[1] 崔连香[1] 刘莉[1] 刘耀斌 YAN Li-mei;ZHAO Lin-lin;CUI Lian-xiang;LIU Li;LIU Yao-bin(School of Mathematics and Big Data,Dezhou University,Dezhou Shandong 253000,China)

机构地区：[1]德州学院数学与大数据学院,山东德州253000

出　　处：《德州学院学报》2023年第2期5-11,共7页Journal of Dezhou University

摘　　要：本文研究了Sylvester四元数矩阵方程A_(1)X_(1)B_(1)+A_(2)X_(2)B_(2)=C的最小二乘Hankel解的问题。将四元数矩阵的实向量表示方法和矩阵的半张量积方法联合起来,将所研究的四元数问题转化为实矩阵方程。根据Hankel矩阵的结构特征,提取了矩阵中的有效元素,构造了新的解向量,降低了所研究问题的复杂度。得到了方程存在Hankel解的条件,并给出Hankel解的一般形式。最后,给出了求解所讨论问题的算法。Least square Hankel solutions of the Sylvester quaternion matrix equation A_(1)X_(1)B_(1)+A_(2)X_(2)B_(2)=C are studied.By means of real vector representation of qua ternion matrix and semi sensor product theory,the quaternion matrix equation is transformed into its equivalent real matrix equation.Considered the structural characteristics of Hankel matrix,independent elements of the solution matrix are extracted to reconstruct a new solution vector,thus the computational complexity of the problem is reduced.The existing conditions of Hankel solutions of the equation are obtained and the general solutions of the equation are given.Finally,the algorithm finding the solution of the discussed problem is provided.

关 键 词：Sylvester四元数矩阵方程 矩阵的半张量积 最小二乘Hankel解 

分 类 号：O241.6[理学—计算数学]