子矩阵约束下三类矩阵方程的迭代解法  

Iterative Solutions of Three Kinds of Matrix Equations with Sub-matrix Restrains

作　　者：黄雅[1] 周富照[1] 郭婧[1] 

机构地区：[1]长沙理工大学数学与计算科学学院,湖南长沙410076

出　　处：《汕头大学学报（自然科学版）》2009年第1期1-7,共7页Journal of Shantou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10671026;60572114)

摘　　要：讨论了子矩阵约束下三类矩阵方程的双反对称迭代解.利用广义共轭梯度法构造迭代算法,并证明了算法的有限步终止性.所得算法能自动判定解的情况.当矩阵方程(组)相容时,得到矩阵方程(组)的解;当矩阵方程(组)不相容时,得到矩阵方程(组)的最小二乘解.Solutions of three kinds of matrix equations with sub-matrix restrains on bi-antisymmetric matrix set were investigated. Iterative methods by the generalized conjugate gradient method were constructed and its limited termination was proved. The method can judge automatically the information of solutions. When the equation（equations） is consistent, the iterative solutions converge to the solutions of the equation（equations）. When the equation （equations） is inconsistent, the iterative solutions converge to the least-squares solutions of the equation（equations）.

关 键 词：子矩阵约束 矩阵方程 迭代解法 有限终止性 

分 类 号：O241.6[理学—计算数学]