矩阵方程AXA^T+BYB^T+AZB^T=D的(局部)对称最小二乘解  

The Least Squares (Locally) Symmetric Solutions of the Matrix Equation AXA^T+BYB^T+AZB^T=D

作　　者：孙庆娟[1,2] 郭文彬[1] 江春林[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059 [2]潍坊市寒亭区第一中学,山东潍坊261100

出　　处：《烟台大学学报（自然科学与工程版）》2013年第1期4-8,共5页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11076015)

摘　　要：矩阵方程问题在结构设计、系统识别、振动理论等领域有着广泛的应用.对于任意给定的矩阵A∈Rm×n,B∈Rm×n,D∈Rm×m,本文利用奇异值分解和Kronecker积给出了矩阵方程AXAT+BYBT+AZBT=D的局部对称最小二乘解,并在一定条件下得出了方程的对称最小二乘解.The matrix equation problem has been widely used in many fields such as structure design, system iden- tification, vibration theory and so on. For given matrices ,A RTM ,B ∈ R ,D ∈R , the least squares locally symmetric solutions of the matrix equation AXAT ＋ BYBT ＋AZBT =D are obtained by using the singular value de- composition and the Kroneeker product of matrices. Under certain conditions, we also give the least squares sym- metric solutions of the preceding matrix equation.

关 键 词：奇异值分解 KRONECKER积 对称矩阵 最小二乘解 

分 类 号：O151.21[理学—数学]