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Summary: Approximation of large-scale dynamical systems: An overview
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A.C. Antoulas£ and D.C. Sorensen¤
August 31, 2001
Abstract
In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish
among three basic categories, namely the SVD-based, the Krylov-based and the SVD-Krylov-based approxi-
mation methods. The first two were developed independently of each other and have distinct sets of attributes
and drawbacks. The third approach seeks to combine the best attributes of the first two.
Contents
1 Introduction and problem statement 1
2 Motivating Examples 3
3 Approximation methods 4
3.1 SVD-based approximation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1.1 The Singular value decomposition: SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1.2 Proper Orthogonal Decomposition (POD) methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.3 Approximation by balanced truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.4 Computation of the singular values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.5 Other types of balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.6 Hankel norm approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
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