On optimality of approximate low rank solutions of large-scale matrix equations

被引：10

作者：

Benner, Peter ^{[1
,2
]}

Breiten, Tobias ^{[1
,3
]}

机构：

[1] Max Planck Inst Dynam Complex Tech Syst, D-39106 Magdeburg, Germany

[2] TU Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[3] Karl Franzens Univ Graz, Inst Math & Sci Comp, A-8010 Graz, Austria

来源：

SYSTEMS & CONTROL LETTERS | 2014年 / 67卷

关键词：

Matrix equations; Low rank approximations; Rational Krylov subspaces; H-2-model reduction; H-2; MODEL-REDUCTION; KRYLOV SUBSPACE; LYAPUNOV;

D O I：

10.1016/j.sysconle.2014.02.005

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we discuss some optimality results for the approximation of large-scale matrix equations. In particular, this includes the special case of Lyapunov and Sylvester equations, respectively. We show a relation between the iterative rational Krylov algorithm and a Riemannian optimization method which recently has been shown to locally minimize a certain energy norm of the underlying Lyapunov operator. Moreover, we extend the results for a more general setting leading to a slight modification of IRKA. By means of some numerical test examples, we show the efficiency of the proposed methods. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：55 / 64

页数：10

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