| 周烁,杨士通,王雯.矩阵方程组$AX=B,XC=D$的Hermitian自反(反Hermitian自反)最小二乘解及其最佳逼近[J].数学研究及应用,2011,31(6):1108~1116 |
| 矩阵方程组$AX=B,XC=D$的Hermitian自反(反Hermitian自反)最小二乘解及其最佳逼近 |
| Least-Squares Solutions of Matrix Equations $(AX=B, XC=D)$ for Hermitian Reflexive (Anti-Hermitian Reflexive) Matrices and Its Approximation |
| 投稿时间：2010-06-12 修订日期：2011-01-12 |
| DOI：10.3770/j.issn:1000-341X.2011.06.020 |
| 中文关键词: 矩阵方程组 Hermitian自反矩阵 反Hermitian自反矩阵 最小二乘解 最佳逼近. |
| 英文关键词:matrix equations Hermitian reflexive matrix Anti-Hermitian reflexive matrix least-squares solution optimal approximation. |
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| 中文摘要: |
| 本文主要研究了矩阵方程组$AX=B,XC=D$的Hermitian自反（反Hermitian自反）最小二乘解，利用分块矩阵和Hermitian自反（反Hermitian自反）矩阵的性质，给出解的一般表示形式。此外，研究了与给定矩阵的最佳逼近问题。 |
| 英文摘要: |
| In this paper, the Hermitian reflexive (Anti-Hermitian reflexive) least-squares solutions of matrix equations $(AX=B, XC=D)$ are considered. With special properties of partitioned matrices and Hermitian reflexive (Anti-Hermitian reflexive) matrices, the general expression of the solution is obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is considered. |
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