| 一种求矩阵方程AXB=C最小二乘对称解的迭代法 |
| |
| 引用本文： | 彭卓华.一种求矩阵方程AXB=C最小二乘对称解的迭代法[J].赣南师范学院学报,2008,29(3):15-17. |
| |
| 作者姓名： | 彭卓华 |
| |
| 作者单位： | 湖南科技大学数学与计算科学学院,湖南,湘潭,411201 |
| |
| 摘 要： | 提出一种迭代法求最小二乘问题min‖AXB-C‖的对称解.通过这种方法,给定初始对称矩阵X1,在没有舍入误差的情况下,经过有限步迭代,找到它的一个对称解.并且,通过选择一种特殊的初始对称矩阵,得到它的最小范数对称解X^＊.另外,给定矩阵X0,通过求解最小二乘问题min‖AXB-C‖（其中C=C-AX0B）,得到它的最佳逼近对称解.
|
| 关 键 词： | 迭代法 矩阵方程 对称解 最小范数解 |
An Iterative Method for the Least Squares Symmetric Solution of the Matrix Equation AXB=C |
| |
| PENG Zhuo-hua.An Iterative Method for the Least Squares Symmetric Solution of the Matrix Equation AXB=C[J].Journal of Gannan Teachers' College(Social Science(2)),2008,29(3):15-17. |
| |
| Authors: | PENG Zhuo-hua |
| |
| Institution: | PENG Zhuo-hua (College of Mathematics, Hunan University of Science and Technology, Xiangtan 411201, China) |
| |
| Abstract: | In this paper, an algorithm is presented to solve the symmetric solution of the minimum Frobenius norm residual problem: min‖AXB-C‖ . By this algorithm, for any initial symmetric matrix X1, a solution X* can be obtained within finite iteration steps in the absence of roundoff errors, and the solution X* with least norm can be obtained by choosing a special kind of initial symmetric matrix. In addition, the unique optimal approximation solution X^ to a given matrix X0 in Frobenius norm can be obtained by finding the least norm symmetric solution * of the new minimum residual problem: min‖AB-‖ , where =C-AX0B. |
| |
| Keywords: | iterative method matrix equation symmetric solution least-norm solution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
