Li, Fan-Liang; Hu, Xi-Yan; Zhang, Lei The generalized anti-reflexive solutions for a class of matrix equations \((BX=C,XD=E)\). (English) Zbl 1157.15013 Comput. Appl. Math. 27, No. 1, 31-46 (2008). Authors’ summary: The generalized anti-reflexive solution for matrix equations (\(BX = C\), \(XD = E\)), which arise in left and right inverse eigenpair problems, is considered. With the special properties of generalized anti-reflexive matrices, necessary and sufficient conditions for the solvability and a general expression of the solution are obtained. Furthermore, the related optimal approximation problem to a given matrix over the solution set is solved. In addition, the algorithm and the example to obtain the unique optimal approximation solution are given. Reviewer: Sheng Chen (Harbin) Cited in 10 Documents MSC: 15A24 Matrix equations and identities 15A09 Theory of matrix inversion and generalized inverses Keywords:matrix equations; generalized anti-reflexive solution; optimal approximation; algorithm PDFBibTeX XMLCite \textit{F.-L. Li} et al., Comput. Appl. Math. 27, No. 1, 31--46 (2008; Zbl 1157.15013)