一类矩阵方程组双对称解的修正共轭梯度法  

The Modified Conjugate Gradient Method for the Bisymmetric Solutions of a Class Matrix Equations

作　　者：郑凤芹[1] 张凯院[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《中北大学学报（自然科学版）》2011年第2期128-134,共7页Journal of North University of China(Natural Science Edition)

基　　金：陕西省自然科学基金资助项目(2006A05)

摘　　要：建立了求多变量线性矩阵方程组双对称解的迭代算法.利用该算法不仅可以判断矩阵方程组是否存在双对称解,而且在双对称解存在时选取特殊的初始矩阵,能够在有限步迭代计算之后得到矩阵方程组的极小范数双对称解;同时,能够在矩阵方程组的双对称解集合中求得给定矩阵的最佳逼近矩阵.数值算例表明:迭代算法是有效的.An iterative method was presented to find the bisymmetric solutions of the multivariable linear matrix equations.With this method,the existence of the bisymmetric solutions can be determined,and the minimal-norm bisymmetric solutions can be got by choosing special initial bisymmetric matrices.In addition,the optimal approximation matrices to the given matrices can be obtained in the solutions set of the matrix equations.Numerical experiments proved the effectiveness of the algorithm.

关 键 词：矩阵方程组 双对称矩阵 极小范数双对称解 迭代算法 最佳逼近 

分 类 号：O241.6[理学—计算数学]