子矩阵约束下矩阵方程AX=B的正交投影迭代解法  

ORTHOGONAL PROJECTION ITERATIVE METHOD TO MATRIX EQUATION AX=B WITH A SUBMATRIX CONSTRAINT

作　　者：周富照[1] 邹阳芳 

机构地区：[1]长沙理工大学数学与计算科学学院,长沙410114

出　　处：《高等学校计算数学学报》2015年第4期337-347,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(11371072)

摘　　要：1 引言 记Rm×n为全体m×n阶实矩阵集合；给定矩阵A，B∈Rm×n，记（A，B）=tr（ATB）为矩阵A与B的内积；｜｜A｜｜F=（A,A）=（tr（ATA））为矩阵A的Frobenius范数；vec（A）为矩阵A的拉直向量；A（p1：P2，）为矩阵A的p1行到P2行元素组成的子矩降;In this paper, the orthogonal projection iterative method to matrix equation AX = B with a submatrix constraint and its optimal approximation are studied. First by partitioning the matrices A,X,B, the primitive equation are converted to two independent lower-order equations; Then by using the idea of the orthogonal projection iterative method, the iteration algorithm is constructed, its convergence is proven and the estimation of the convergence rate is derived; Finally some numerical examples are given to verify the effectiveness of this method.

关 键 词：迭代解法 正交投影 矩阵方程 FROBENIUS范数 子矩阵 矩阵A 矩阵集合 元素组成 

分 类 号：O241.5[理学—计算数学] O241.6[理学—数学]