求矩阵方程AXB=C的双对称最小二乘解的迭代算法  

AN ITERATIVE METHOD FOR THE LEAST SQUARES BISYMMETRIC SOLUTION OF THE MATRIX EQUATION AXB=C

作　　者：尚丽娜[1] 张凯院[1] 陈梅枝[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《数值计算与计算机应用》2008年第2期126-135,共10页Journal on Numerical Methods and Computer Applications

基　　金：陕西省自然科学基金(2004CS110002).

摘　　要：基于求解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,建立了求矩阵方程AXB=C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.On the base of conjugate gradient method of solving linear algebraic equations, using special transformation and approximate disposal, an iterative method is presented to solve the least squares bisymmetric solution of the matrix equation AXB = C and its convergence is proved. By this iterative method, the least squares bisymmetric solution can be obtained within finite iterative steps in the absence of round off errors, and the solution with least norm can be got by choosing a special initial bisymmetric matrix. In addition, its optimal approximation matrix to a given matrix can be obtained. Given numerical examples are show that the iterative method is quite efficient.

关 键 词：矩阵方程 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] O151.21[理学—数学]