Singular value decomposition of time-varying matrices

被引：19

作者：

Baumann, M ^{[1
]}

Helmke, U ^{[1
]}

机构：

[1] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany

来源：

FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE | 2003年 / 19卷 / 03期

关键词：

singular value decomposition; time-varying matrices; continuation methods;

D O I：

10.1016/S0167-739X(02)00162-0

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper is concerned with an algorithm to compute the singular value decomposition (SVD) of time-varying square matrices. In a first step we consider the task of diagonalizing symmetric time-varying matrices A(t). A differential equation is proposed, whose solutions asymptotically track the diagonalizing transformation. In particular, perfect matching of the initial conditions is not required and the solutions converge exponentially towards the desired transformation. Then the desired differential equation for tracking the SVD is derived. Robustness of the algorithms is guaranteed by our approach. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：353 / 361

页数：9

共 50 条

[21] Time-varying coherency matrices and spectral coherency matrices
Tudor, T
Vinkler, I
[J]. PURE AND APPLIED OPTICS, 1998, 7 (06): : 1451 - 1457
[22] A Delay Decomposition Approach to the Stability Analysis of Singular Systems with Interval Time-Varying Delay
Jiao, Jianmin
Zhang, Rui
[J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2014, 2014
[23] Stability of Singular NCS with Time-Varying Delay
Dang, Xiangdong
Zhang, Qingling
[J]. CCDC 2009: 21ST CHINESE CONTROL AND DECISION CONFERENCE, VOLS 1-6, PROCEEDINGS, 2009, : 499 - 504
[24] Note on analysis of time-varying singular systems
Murugesan, K.
[J]. Advances in Modelling & Simulation, 1991, 24 (04): : 1 - 5
[25] REGULARIZATIONS OF LINEAR TIME-VARYING SINGULAR SYSTEMS
CAMPBELL, SL
[J]. AUTOMATICA, 1984, 20 (03) : 365 - 370
[26] Singular value decomposition for the Takagi factorization of symmetric matrices
Chebotarev, Alexander M.
Teretenkov, Alexander E.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 234 : 380 - 384
[27] COMPUTING THE SINGULAR VALUE DECOMPOSITION OF A PRODUCT OF 2 MATRICES
HEATH, MT
LAUB, AJ
PAIGE, CC
WARD, RC
[J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1986, 7 (04): : 1147 - 1159
[28] ANALYTICAL SINGULAR VALUE DECOMPOSITION FOR A CLASS OF STOICHIOMETRY MATRICES
Wentz, Jacqueline
Cameron, Jeffrey C.
Bortz, David M.
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2022, 43 (03) : 1109 - 1147
[29] Singular value decomposition of multi-companion matrices
Boshnakov, Georgi N.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 424 (2-3) : 393 - 404
[30] The Lyapunov spectrum of families of time-varying matrices
Colonius, F
Kliemann, W
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (11) : 4389 - 4408

← 1 2 3 4 5 →