迭代法求解约束矩阵方程AXB+CYD=E  

An Iteration Algorithm for Solving Constrained Matrix Equation AXB+CYD =E

作　　者：杜丹丹[1,2] 肖宪伟 彭振赟[1,2] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]广西高校桂林电子科技大学数据分析与计算重点实验室,广西桂林541004

出　　处：《数学理论与应用》2016年第1期61-72,共12页Mathematical Theory and Applications

基　　金：国家自然科学基金资助项目(11261014;11301107;11101100)

摘　　要：约束矩阵方程在自动控制理论、生物学、电学等领域有广泛的应用.本文研究了矩阵元素和特征值区间约束下矩阵方程AXB+CYD=E最小二乘解问题.给出矩阵对(X*,Y*)是问题的解的充分必要条件,给出计算约束解的迭代方法,证明了算法的全局收敛性.The constraint matrix equation problems have been widely used in control theory, biology, electrici- ty and so on. In this paper, we solve the least squares problem of the matrix equation AXB ＋ CYD = E with the matrix element and eigenvalue interval constraints. The necessary and sufficient condition for matrix pair （X＊,Y＊ ） being a solution of the problem is derived. An iteration algorithm to solve the constraint solution is given, and the convergence of the algorithm is showed.

关 键 词：矩阵方程 矩阵不等式 最小二乘问题 迭代算法 

分 类 号：O241.6[理学—计算数学]