求线性矩阵方程双对称最小二乘解的变形共轭梯度法  

The Modified Conjugate Gradient Method for the Least Squares Bisymmetric Solution of the General Linear Matrix Equation

作　　者：田小红[1] 张凯院[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《工程数学学报》2010年第5期827-832,共6页Chinese Journal of Engineering Mathematics

基　　金：陕西省自然科学基金(2006A05)~~

摘　　要：本文基于求线性代数方程组的共轭梯度法的思想,通过特殊的变形与近似处理,建立了求一般线性矩阵方程的双对称最小二乘解的迭代算法,并证明了迭代算法的收敛性。不考虑舍入误差时,迭代算法能够在有限步计算之后得到矩阵方程的双对称最小二乘解;选取特殊的初始矩阵时,还能够求得矩阵方程的极小范数双对称最小二乘解。同时,也能够给出指定矩阵的最佳逼近双对称矩阵。算例表明,迭代算法是有效的。In this paper,an iterative method is proposed to find the least squares bisymmetric solutions of the general linear matrix equation.This method is obtained through a special transformation and the approximate disposal on the base of conjugate gradient method for solving linear algebraic equations. The convergence of this method is also given.By using this method,a least squares bisymmetric solution can be obtained within the finite iterative steps in the absence of round-off errors,and the solution with least norm can be obtained by choosing a special initial bisymmetric matrix.In addition, its optimal approximation solution to a given matrix can be obtained.Numerical examples show that the iterative method is efficient.

关 键 词：双对称矩阵 最小二乘解 极小范数解 迭代算法 最佳逼近 

分 类 号：O241.6[理学—计算数学]