Iterative Hermitian R- conjugate solutions to coupled Sylvester complex matrix equations with conjugate of two unknowns

Abstract

This paper presents an iterative algorithm to solve coupled Sylvester complex matrix equations with conjugate of two unknowns over Hermitian R - conjugate matrices. Necessary and sufficient conditions are given such that the proposed iterative algorithms converge to the exact solution for arbitrary initial Hermitian  R- conjugate solution matrices V1,W1 .  A numerical example verifies the proposed method is given.