AOR Iterative Method for Coupled Lyapunov Matrix Equations

ZHANG Shi-jun , WANG Shi-heng , WANG Ke

doi:10.13371/j.cnki.chin.q.j.m.2021.02.003

Chinese Quarterly Journal of Mathematics >

2021 , Vol. 36 >Issue 2: 141 - 148

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.02.003

AOR Iterative Method for Coupled Lyapunov Matrix Equations

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1. Department of Mathematics, Shanghai University, Shanghai 200444, China; 2. Nanyang Vocational
College of Agriculture, Nanyang 473000, China

ZHANG Shi-jun (1963-), male, native of Nanyang, Henan, associate professor of Nanyang Vocational College of Agriculture, engages in applied mathematics; WANG Shi-heng (1965-), male, native of Nanyang, Henan, professor of Nanyang Vocational College of Agriculture, engages in algebra; Corresponding author: WANG Ke.

Received date: 2020-10-29

Online published: 2021-01-12

Supported by

Supported by Key Scientific Research Project of Colleges and Universities in Henan Province
of China (Grant No. 20B110012).

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Abstract

An AOR (Accelerated Over-Relaxation) iterative method is suggested by
introducing one more parameter than SOR (Successive Over-Relaxation) method for
solving coupled Lyapunov matrix equations (CLMEs) that come from continuous-time
Markovian jump linear systems. The proposed algorithm improves the convergence rate,
which can be seen from the given illustrative examples. The comprehensive theoretical
analysis of convergence and optimal parameter needs further investigation.

Key words： Coupled Lyapunov matrix equations; AOR iterative method; SOR iterative
method; Markovian jump systems

Cite this article

ZHANG Shi-jun , WANG Shi-heng , WANG Ke . AOR Iterative Method for Coupled Lyapunov Matrix Equations[J]. Chinese Quarterly Journal of Mathematics, 2021 , 36(2) : 141 -148 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.003

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