摘要
基于求线性代数方程组的共轭梯度法的思想,建立了求一般线性矩阵方程的自反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自反最小二乘解;选取特殊的初始矩阵时,可求得极小范数自反最小二乘解.同时,也能够给出指定矩阵的最佳逼近自反矩阵.最后,用数值算例对有关结果进行了验证.
On the base of conjugate gradient method of solving linear algebraic equations,an iterative method is presented to find the least squares reflexive solution of the general linear matrix equation and its convergence is proved.By the iterative method,the least squares reflexive solution can be obtained within finite iterative steps in the absence of round off errors.And the least squares solution with minimal norm can be obtained by choosing a special initial reflexive matrix.In addition,its optimal approximation matrix to a given matrix can be obtained.The given numerical examples show that the iterative method is quite efficient.
出处
《中北大学学报（自然科学版）》
CAS
北大核心
2010年第6期548-553,共6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)
关键词
矩阵方程
自反矩阵
最小二乘解
极小范数解
迭代算法
最佳逼近
matrix equation
reflexive matrix
least squares solution
minimal-norm solution
iterative method
optimal approximation
