Generalized Reflexive and Generalized Antireflexive Solutions to a System of Matrix Equations

Abstract

Two efficient iterative algorithms are presented to solve a system of matrix equations $A_1{X}_1{B}_1$ + $A_2{X}_2{B}_2$ $=E$, $C_1{X}_1{D}_1$ + $C_2{X}_2{D}_2$ $=F$ over generalized reflexive and generalized antireflexive matrices. By the algorithms, the least norm generalized reflexive (antireflexive) solutions and the unique optimal approximation generalized reflexive (antireflexive) solutions to the system can be obtained, too. For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values. The given numerical examples demonstrate that the iterative algorithms are efficient.