| 矩阵方程A~TXA=B的双反对称最小二乘解及其最佳逼近 |
| |
| 引用本文： | 李水勤,邓继恩,杨娟.矩阵方程A~TXA=B的双反对称最小二乘解及其最佳逼近[J].信阳师范学院学报(自然科学版),2011,24(2):183-187. |
| |
| 作者姓名： | 李水勤 邓继恩 杨娟 |
| |
| 作者单位： | 1. 河南理工大学,数学与信息科学学院,河南焦作454003
2. 河南理工大学,物理化学学院,河南焦作454003 |
| |
| 基金项目： | 河南省教育厅自然科学研究计划项目 |
| |
| 摘 要： | 利用矩阵对的标准相关分解、广义奇异值分解和投影定理,给出了矩阵方程ATXA=B的双反对称最小二乘解的一般表达式,在此基础上,求出了给定矩阵的最佳逼近.
|
| 关 键 词： | 双反对称矩阵 标准相关分解 广义奇异值分解 最小二乘解 最佳逼近解 |
Least-squares Solutions of Anti-bisymmetric Matrices to Matrix Equation ATXA = B and Their Optimal Approximation |
| |
| LI Shui-qin,DENG Ji-en,YANG Juan.Least-squares Solutions of Anti-bisymmetric Matrices to Matrix Equation ATXA = B and Their Optimal Approximation[J].Journal of Xinyang Teachers College(Natural Science Edition),2011,24(2):183-187. |
| |
| Authors: | LI Shui-qin DENG Ji-en YANG Juan |
| |
| Institution: | LI Shui-qina,DENG Ji-ena,YANG Juanb(a.School of Mathematics and Information Science,b.Department of Physics and Chemistry,Henan Polytechnic University,Jiaozuo 454003,China) |
| |
| Abstract: | According to the canonical correlation decomposition of a pair of matrices,generalized singular value decomposition and the projection theorem,the expression of the least-squares solutions of anti-bisymmetric matrices to matrix equation ATXA=B is given.Based on this result,the optimal approximate solution to a given matrix is also derived. |
| |
| Keywords: | anti-bisymmetric matrix canonical correlation decomposition generalized singular value decomposition least-squares solution optimal approximate solution |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
