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

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 arbi-trary initial matrices. Further, we apply the MRGI algorithm to study a more general coupled Sylvester conjugate matrix equations and give a sufficient con-dition to guarantee that the iterative solution converges to the exact solution. Two numerical experiments are provided to demonstrate that the MRGI al-gorithm 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.

Automated summary

This paper proposes a modified relaxed gradient based iterative (MRGI) algorithm for solving the coupled Sylvester-conjugate matrix equations (CSCMEs) based on the hierarchical identification principle. The convergence analysis shows that the proposed algorithm is effective for any initial matrices. Furthermore, the MRGI algorithm is applied to a more general case of CSCMEs and a sufficient condition is provided to guarantee the convergence of the iterative solution to the exact solution. Numerical experiments demonstrate that the MRGI algorithm outperforms three existing algorithms in terms of efficiency and accuracy, which were presented by Wu et al. (2010) and Huang and Ma (2018). Additionally, an application of the MRGI algorithm in discrete-time antilinear system is derived.