A NOVEL ITERATIVE METHOD FOR SOLVING THE COUPLED SYLVESTER-CONJUGATE MATRIX EQUATIONS AND ITS APPLICATION IN ANTILINEAR SYSTEM

Abstract

This paper is devoted to constructing a modified relaxed gradient based iterative (MRGI) algorithm to solve the coupled Sylvester-conjugate matrix equations (CSCMEs) based on the hierarchical identification principle. Convergence analysis shows that the proposed algorithm is effective for arbitrary initial matrices. Further, we apply the MRGI algorithm to study a more general coupled Sylvester conjugate matrix equations and give a sufficient condition to guarantee that the iterative solution converges to the exact solution. Two numerical experiments are provided to demonstrate that the MRGI algorithm has better efficiency and accuracy than the three existing algorithms, which are presented by Wu et al. (2010) and Huang and Ma (2018). Finally, we derive an application of MRGI algorithm in discrete-time antilinear system.