Coupled iterative algorithms based on optimisation for solving Sylvester matrix equations

摘要

In this study, novel iterative algorithms based on optimisation are developed to solve the continuous-time and discrete-time Sylvester matrix equations. The great difference of the proposed algorithms is that solutions of the equations are updated by two different sequences generated by the proposed algorithms. Convergence rates of the proposed algorithms can be markedly improved by choosing appropriate tuning parameters. Convergence conditions of the proposed algorithms are provided for different cases. Moreover, efficient numerical methods are presented to find the appropriate tuning parameters. Finally, three examples are given to illustrate the effectiveness of the proposed algorithms, and to compare the convergence performance of different algorithms.