article

Interpolatory Projection Methods for Parameterized Model Reduction

Authors:

Christopher Beattie,

Serkan GugercinAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 33, Issue 5

Pages 2489 - 2518

https://doi.org/10.1137/090776925

Published: 01 October 2011 Publication History

Abstract

We provide a unifying projection-based framework for structure-preserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order model. The parameter dependence may be linear or nonlinear and is retained in the reduced-order model. Moreover, we are able to give conditions under which the gradient and Hessian of the system response with respect to the system parameters is matched in the reduced-order model. We provide a systematic approach built on established interpolatory $\mathcal{H}_2$ optimal model reduction methods that will produce parameterized reduced-order models having high fidelity throughout a parameter range of interest. For single input/single output systems with parameters in the input/output maps, we provide reduced-order models that are optimal with respect to an $\mathcal{H}_2\otimes\mathcal{L}_2$ joint error measure. The capabilities of these approaches are illustrated by several numerical examples from technical applications.

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cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 33, Issue 5

^† Special Section: 2010 Copper Mountain Conference

2011

972 pages

ISSN:1064-8275

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Society for Industrial and Applied Mathematics

United States

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Published: 01 October 2011

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https://dl.acm.org/doi/10.1016/j.cam.2024.115844
Borghi ABreiten T(2024) optimal rational approximation on general domainsAdvances in Computational Mathematics10.1007/s10444-024-10125-850:3Online publication date: 1-Jun-2024
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