实子矩阵约束下矩阵方程AX=B的共轭梯度迭代解法  

Conjugate Gradient Method to the Matrix Equation AX=B with a Real Submatrix Constraint

作　　者：邹阳芳 周富照[1] 田时宇[1] 

机构地区：[1]长沙理工大学数学与计算科学学院

出　　处：《数学理论与应用》2014年第1期12-17,共6页Mathematical Theory and Applications

基　　金：国家自然科学基金资助项目(批准号11371072)

摘　　要：本文研究了实子矩阵约束下矩阵方程AX=B及其最佳逼近的共轭梯度迭代解法.首先运用矩阵分块将原方程AX=B转换为2个低阶方程,利用共轭梯度的思想构造迭代算法;然后证明了算法的有限步终止性;最后给出数值实例验证算法的有效性.In this paper, the conjugate gradient method to the matrix equation AX = B with a real submatrix con- straint and its optimal approximation solution is studied. Firstly, by partitioning matrixA, X, B, the primary equation AX = B is converted to two lower - order equations ; by using the idea of the conjugate gradient method, the iteration algorithm is constructed. Then its limited termination is proven. Finally some numerical examples are given to verify the effectiveness of this method.

关 键 词：子矩阵约束 共轭梯度迭代法 有限步终止性 最佳逼近 

分 类 号：O241.6[理学—计算数学]