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【答案】应助回帖
★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
感谢参与，应助指数 +1
xinren08: 金币+50, ★★★★★最佳答案 2020-11-07 22:34:03
sunshan4379: LS-EPI+1, 感谢应助! 2020-11-16 20:27:38
Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations (Open Access)
Accession number: 20201008257555
Authors: Sun, Min 1 ; Liu, Jing 2
Author affiliations : 1 School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, Shandong; 277160, China
2 School of Date Scineces, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang, China
Corresponding author: Sun, Min (ziyouxiaodou@163.com)
Source title: Mathematical Problems in Engineering
Abbreviated source title: Math. Probl. Eng.
Volume: 2020
Issue date: 2020
Publication Year: 2020
Article number: 6968402
Language: English
ISSN: 1024123X
E-ISSN: 15635147
Document type: Journal article (JA)
Publisher: Hindawi Limited, 410 Park Avenue, 15th Floor, 287 pmb, New York, NY 10022, United States
Abstract: It is well-known that the stability of a first-order autonomous system can be determined by testing the symmetric positive definite solutions of associated Lyapunov matrix equations. However, the research on the constrained solutions of the Lyapunov matrix equations is quite few. In this paper, we present three iterative algorithms for symmetric positive semidefinite solutions of the Lyapunov matrix equations. The first and second iterative algorithms are based on the relaxed proximal point algorithm (RPPA) and the Peaceman-Rachford splitting method (PRSM), respectively, and their global convergence can be ensured by corresponding results in the literature. The third iterative algorithm is based on the famous alternating direction method of multipliers (ADMM), and its convergence is subsequently discussed in detail. Finally, numerical simulation results illustrate the effectiveness of the proposed iterative algorithms.
© 2020 Min Sun and Jing Liu.
Number of references: 24
Main heading: Iterative methods
Controlled terms: Matrix algebra - Well testing
Uncontrolled terms: Alternating direction method of multipliers - Autonomous systems - Global conver-gence - Iterative algorithm - Lyapunov matrix equations - Positive semidefinite - Proximal point algorithm - Symmetric positive definite
Classification code: 921.1 Algebra - 921.6 Numerical Methods
DOI: 10.1155/2020/6968402
Funding Details:
NumberAcronymSponsorZR2016AL05-Natural Science Foundation of Shandong Province
Funding text:
This research was partially supported by the National Natural Science Foundation of Shandong Province (no. ZR2016AL05)
Database: Compendex
Compilation and indexing terms, © 2020 Elsevier Inc. |
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