摘要
本文建立了求矩阵方程AXB=C的中心对称最小二乘解的迭代算法。在不考虑舍入误差时,对任意给定的初始中心对称矩阵,该算法能够在有限步迭代后得到此方程的中心对称最小二乘解。当选取特殊的初始矩阵时,可得到极小范数中心对称最小二乘解。另外,在上述解集合中也可得到给定矩阵的最佳逼近矩阵的表达式。
An iterative method is presented to solve the least squares central symmetric solutions of the matrix equation AXB = C. By this iterative method, for any initial central symmetric matrix, a solution can be obtained within finite iterative steps in the absence of round-off errors, and the solution with least norm can be obtained by choosing a special kind of initial central symmetric matrices. In addition, its optimal approximation solution to a given matrix can be obtained.
出处
《工程数学学报》
CSCD
北大核心
2008年第6期1125-1128,共4页
Chinese Journal of Engineering Mathematics
基金
陕西省自然科学基金(2004CS110002)
关键词
矩阵方程
迭代算法
中心对称矩阵
最小二乘解
最佳逼近
matrix equation
iterative method
central symmetric matrix
least squares solution
optimal approximation
