Matrix inverse problem and its optimal approximation problem for R-symmetric matrices

Abstract: Let be a nontrivial involution, i.e., and . A matrix is called R-symmetric if . The solvability conditions and the expression of the matrix inverse problem for R-symmetric matrices with are derived, also the least-squares solutions of the matrix inverse problem for R-symmetric matrices with are given. The corresponding optimal approximation problem for R-symmetric matrices with is considered. We firstly point out that the optimal approximation problem is solvable, then get the expression of its unique solution. It can be seen that this paper generalizes the results mentioned in Zhou [F.-Z. Zhou, L. Zhang, X.-Y. Hu, Least-square solutions for inverse problem of centrosymmetric matrices, Comput. Math. Appl. 45 (2003) 1581–1589]. [Copyright &y& Elsevier]