Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices

• Autor(a) principal: Dehghan,Mehdi
• Data de Publicação: 2012
• Outros Autores: Hajarian,Masoud
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Computational & Applied Mathematics
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022012000200008
• topic: iterative algorithm; matrix equation; reflexive matrix; anti-reflexive matrix

An n × 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 ∈ 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 + 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.