%0 Journal Article
%T Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices
%A Mehdi Dehghan
%A Masoud Hajarian
%J Computational and Applied Mathematics
%D 2012
%I 
%R 10.1590/s1807-03022012000200008
%X An n ¡Á n real matrix P is said to be a generalized reflection matrix if P T = P and P2 = I (where P T is the transpose of P). A matrix A ¡Ê Rn¡Án is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = P A P (A = - P A P). The reflexive and anti-reflexive matrices have wide applications in many fields. In this article, two iterative algorithms are proposed to solve the coupled matrix equations { A1 XB1 + C1X T D1 = M1. A2 XB2 + C2X T D2 = M2. over reflexive and anti-reflexive matrices, respectively. We prove that the first (second) algorithm converges to the reflexive (anti-reflexive) solution of the coupled matrix equations for any initial reflexive (anti-reflexive) matrix. Finally two numerical examples are used to illustrate the efficiency of the proposed algorithms. Mathematical subject classification: 15A06, 15A24, 65F15, 65F20.
%K iterative algorithm
%K matrix equation
%K reflexive matrix
%K anti-reflexive matrix
%U http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022012000200008