Gradient based iterative solutions for general linear matrix equations

被引：177

作者：

Xie, Li ^{[1
]}

Ding, Jie ^{[1
]}

Ding, Feng ^{[1
]}

机构：

[1] Jiangnan Univ, Sch Commun & Control Engn, Wuxi 214122, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2009年 / 58卷 / 07期

关键词：

Lyapunov matrix equations; Sylvester matrix equations; Iterations; Least-squares; Estimation; LEAST-SQUARES SOLUTIONS; IDENTIFICATION METHODS; PERFORMANCE ANALYSIS; NUMERICAL ALGORITHM; SYSTEMS;

D O I：

10.1016/j.camwa.2009.06.047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a gradient based iterative algorithm for solving general linear matrix equations by extending the Jacobi iteration and by applying the hierarchical identification principle. Convergence analysis indicates that the iterative solutions always converge fast to the exact solutions for any initial values and small condition numbers of the associated matrices. Two numerical examples are provided to show that the proposed algorithm is effective. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1441 / 1448

页数：8

共 21 条

[1] Some new connections between matrix products for partitioned and non-partitioned matrices
Al Zhour, Zeyad
Kilicman, Adem
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (06) : 763 - 784
[2] An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation
Dehghan, Mehdi
Hajarian, Masoud
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 202 (02) : 571 - 588
[3] On iterative solutions of general coupled matrix equations
Ding, F
Chen, TW
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 44 (06) : 2269 - 2284
[4] Gradient based iterative algorithms for solving a class of matrix equations
Ding, F
Chen, TW
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (08) : 1216 - 1221
[5] Hierarchical gradient-based identification of multivariable discrete-time systems
Ding, F
Chen, TW
[J]. AUTOMATICA, 2005, 41 (02) : 315 - 325
[6] Hierarchical least squares identification methods for multivariable systems
Ding, F
Chen, TW
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (03) : 397 - 402
[7] Iterative least-squares solutions of coupled Sylvester matrix equations
Ding, F
Chen, TW
[J]. SYSTEMS & CONTROL LETTERS, 2005, 54 (02) : 95 - 107
[8] Parameter identification and intersample output estimation for dual-rate systems
Ding, Feng
Liu, Peter X.
Yang, Huizhong
[J]. IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS, 2008, 38 (04): : 966 - 975
[9] Performance analysis of stochastic gradient algorithms under weak conditions
Ding Feng
Yang HuiZhong
Liu Fei
[J]. SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES, 2008, 51 (09): : 1269 - 1280
[10] Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
Ding, Feng
Liu, Peter X.
Ding, Jie
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 197 (01) : 41 - 50

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