Convergence of the Iterative Rational Krylov Algorithm

被引：35

作者：

Flagg, Garret ^{[1
]}

Beattie, Christopher ^{[1
]}

Gugercin, Serkan ^{[1
]}

机构：

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

来源：

SYSTEMS & CONTROL LETTERS | 2012年 / 61卷 / 06期

关键词：

Rational Krylov; H-2; approximation; Interpolation; MODEL-REDUCTION; APPROXIMATION;

D O I：

10.1016/j.sysconle.2012.03.005

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The iterative rational Krylov algorithm (IRKA) of Gugercin et al. (2008) [8] is an interpolatory model reduction approach to the optimal H-2 approximation problem. Even though the method has been illustrated to show rapid convergence in various examples, a proof of convergence has not been provided yet. In this note, we show that in the case of state-space-symmetric systems. IRKA is a locally convergent fixed-point iteration to a local minimum of the underlying H-2 approximation problem. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：688 / 691

页数：4

共 22 条

[1]

Antoulas. A. C., 2005, Adv. Des. Control

[2]

Beattie C., 48 IEEE C DEC CONTR

[3]

Beattie C. A., 2007, 46 IEEE C DEC CONTR, P4385

[4] SOLUTION OF LARGE SCALE EVOLUTIONARY PROBLEMS USING RATIONAL KRYLOV SUBSPACES WITH OPTIMIZED SHIFTS [J].