Open AccessCoupled iterative algorithms based on optimisation for solving Sylvester matrix equations
Author(s) -
Zhang Wenxue,
Zhou Di
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5151
Subject(s) - sylvester matrix , sylvester equation , algorithm , convergence (economics) , matrix (chemical analysis) , computer science , iterative method , rate of convergence , mathematical optimization , mathematics , key (lock) , eigenvalues and eigenvectors , mathematical analysis , physics , materials science , computer security , matrix polynomial , quantum mechanics , polynomial matrix , polynomial , economics , composite material , economic growth
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.