求解矩阵方程组A1XB1+C1XD1=E1,A2XB2+C2XD2=E2的迭代算法  

An Iterative Algorithm for Solutions of the System of Matrix Equations A1XB1+C1XD1=E1,A2XB2+C2XD2=E2

作　　者：周海林[1] 王娅[1] 叶建兵[1] 刘大瑾[1] 谭沈阳[1] ZHOU HAILIN;WANG YA;YE JIANBING;LIU DAJIN;TAN SHENGYANG(Taizhou Institute of Sci.＆ Tech.,NUST.,Taizhou 225300,China)

机构地区：[1]南京理工大学泰州科技学院

出　　处：《应用数学学报》2018年第5期577-588,共12页Acta Mathematicae Applicatae Sinica

基　　金：江苏省高等学校自然科学研究面上项目(17KJD110004)资助

摘　　要：应用共轭梯度方法和线性投影算子,给出迭代算法求解了线性矩阵方程组A1XB1＋C1XD1=E1,A2XB2＋C2XD2=E2在任意线性子空间上的约束解及其最佳逼近.可以证明,当矩阵方程组A1XB1＋C1XD1=E1,A2XB2＋C2XD2=E2相容时,所给迭代算法经过有限步迭代可得到矩阵方程组的约束解,极小范数解和最佳逼近.文中的数值例子证实了该算法的有效性.Applying the conjugate gradient method and linear projection operator, an iterative algorithm is presented to solve the system of linear matrix equations A1XB1＋C1XD1=E1, A2XB2＋C2XD2=E2 for constrained solution and its optimal approximation over any linear subspace. It is proved that the constrained solution, the least-norm solution and the optimal approximation of the system of matrix equations can be obtained within finite iteration steps by the method while the system of matrix equations A1XB1＋C1XD1=E1, A2XB2＋C2XD2=E2 is consistent. The numerical example verifies the efficiency of the algorithm.

关 键 词：共轭梯度 投影算子 极小范数解 最佳逼近 

分 类 号：O151.21[理学—数学]