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Computational & Applied Mathematics

On-line version ISSN 1807-0302

Abstract

DEHGHAN, Mehdi  and  HAJARIAN, Masoud. Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices. Comput. Appl. Math. [online]. 2012, vol.31, n.2, pp. 353-371. ISSN 1807-0302.  http://dx.doi.org/10.1590/S1807-03022012000200008.

An n × n real matrix P is said to be a generalized reflection matrix if PT = P and P2 = I (where PT is the transpose of P). A matrix A ∈ Rn×n 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 + C1XTD1 = M1. A2 XB2 + C2XTD2 = 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.

Keywords : iterative algorithm; matrix equation; reflexive matrix; anti-reflexive matrix.

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