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

AUTOR(ES)

Dehghan, Mehdi, Hajarian, Masoud

FONTE

Comput. Appl. Math.

DATA DE PUBLICAÇÃO

2012

RESUMO

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.

Documentos Relacionados

• The generalized anti-reflexive solutions for a class of matrix equations (BX = C, XD = E)
• An iterative method for solving a kind of constrained linear matrix equations system
• Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations
• Two derivative-free methods for solving underdetermined nonlinear systems of equations
• Algorithms and Properties for Positive Symmetrizable Matrices