子矩阵约束下三类矩阵方程的对称正交对称迭代解法  

Iterative methods for three kinds of matrix equations with sub-matrix restrains on symmetric ortho-symmetric matrix set

作　　者：周富照[1] 黄雅[1] 

机构地区：[1]长沙理工大学数学与计算科学学院

出　　处：《长沙交通学院学报》2008年第4期87-92,共6页Journal of Changsha Communications University

基　　金：国家自然科学基金资助项目(1067102660572114)

摘　　要：讨论了子矩阵约束下三类矩阵方程的对称正交对称迭代解,利用广义共轭梯度法构造了迭代算法,并证明了算法的有限终止性.该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.Iterative solutions of three kinds of matrix equations with sub-matrix restrains on symmetric ortho- symmetric matrix set are investigated, and iterative method by the generalized conjugate gradient method is constructed, and its limited termination is proved. The information of solutions can automatically be judged by this method. When the equation （equations） is consistent, the solutions of the equation （equations） can be obtained. When the equation （equations） is inconsistent, the least-squares solutions of the equation （ equations） can be obtained.

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]