用矩阵分解求混合Sylvester矩阵方程的最小二乘解  

Least-squares solution of the mixed Sylvester matrix equations by matrix decompositions

作　　者：陈敬华 徐望斌 CHEN Jing-hua;XU Wang-bin(College of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《湖北师范大学学报（自然科学版）》2018年第2期1-7,共7页Journal of Hubei Normal University：Natural Science

摘　　要：通过矩阵对的广义奇异值分解(GSVD)及标准相关分解(CCD),给出了混合Sylvester矩阵方程的最小二乘解.据此,建立了混合Sylvester矩阵方程可解性充要条件并给出了通解的显示表示.By applying the generalized singular value decomposition（ GSVD） and the canonical correlation decomposition（ CCD） of matrix pairs,the least-squares solution of the mixed Sylvester matrix equations is given. Also,the necessary and sufficient solvability condition for the mixed Sylvester equations is established and the explicit representation of the general solution is provided.

关 键 词：Sylvester矩阵方程 最小二乘解 广义奇异值分解 标准相关分解 

分 类 号：O241[理学—计算数学]