耦合Lyapunov 矩阵方程的AOR迭代法

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

数学季刊 ›› 2021, Vol. 36 ›› Issue (2): 141-148.doi: 10.13371/j.cnki.chin.q.j.m.2021.02.003

耦合Lyapunov 矩阵方程的AOR迭代法

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

收稿日期:2020-10-29 出版日期:2021-06-30 发布日期:2021-04-12
作者简介: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.
基金资助:
Supported by Key Scientific Research Project of Colleges and Universities in Henan Province
of China (Grant No. 20B110012).

AOR Iterative Method for Coupled Lyapunov Matrix Equations

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

Received:2020-10-29 Online:2021-06-30 Published:2021-04-12
About author: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.
Supported by:
Supported by Key Scientific Research Project of Colleges and Universities in Henan Province
of China (Grant No. 20B110012).

摘要/Abstract

摘要： 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.

关键词: Coupled Lyapunov matrix equations, AOR iterative method, SOR iterative
method, Markovian jump systems

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

中图分类号:

O241.6

张士君, 王世恒, 王珂. 耦合Lyapunov 矩阵方程的AOR迭代法[J]. 数学季刊, 2021, 36(2): 141-148.

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.

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耦合Lyapunov 矩阵方程的AOR迭代法

AOR Iterative Method for Coupled Lyapunov Matrix Equations

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