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

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.

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.