Algorithms for model reduction of large dynamical systems

作     者：Penzl, Thilo 

作者机构：Univ Calgary Dept Math & Stat Calgary AB T2N 1N4 Canada 

出 版 物：《LINEAR ALGEBRA AND ITS APPLICATIONS》 (线性代数及其应用)

年 卷 期：2006年第415卷第2-3期

页      面：322-343页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Deutscher Akademischer Austauschdienst  DAAD 

主　　题：dynamical systems Lyapunov equation model reduction balanced truncation Schur method square root method numerical algorithms sparse matrices 

摘      要：Three algorithms for the model reduction of large-scale, continuous-time, time-invariant, linear, dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described. They rely on low rank approximations to the controllability and observability Gramians, which can efficiently be computed by ADI based iterative low rank methods. The first two model reduction methods are closely related to the well-known square root method and Schur method, which are balanced truncation techniques. The third method is a heuristic, balancing-free technique. The performance of the model reduction algorithms is studied in numerical experiments. (c) 2006 Elsevier Inc. All rights reserved.