Least-Squares Solutions of Matrix Equations $(AX=B, XC=D)$ for Hermitian Reflexive (Anti-Hermitian Reflexive) Matrices and Its Approximation
Received:June 12, 2010  Revised:January 12, 2011
Key Words: matrix equations   Hermitian reflexive matrix   Anti-Hermitian reflexive matrix   least-squares solution   optimal approximation.  
Fund Project:
Author NameAffiliation
Shuo ZHOU School of Mathematical Sciences, Northeast Dianli University, Jilin 132012, P. R. China 
Shi Tong YANG School of Mathematical Sciences, Northeast Dianli University, Jilin 132012, P. R. China 
Wen WANG School of Mathematical Sciences, Northeast Dianli University, Jilin 132012, P. R. China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.06.020
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