Inexact solves in interpolatory model reduction
| Autor: | Serkan Gugercin, Christopher Beattie, Sarah Wyatt |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Petrov–Galerkin method MathematicsofComputing_NUMERICALANALYSIS Perturbation (astronomy) 010103 numerical & computational mathematics 02 engineering and technology Dynamical Systems (math.DS) 01 natural sciences Reduced order Mathematics::Numerical Analysis 020901 industrial engineering & automation Tangential interpolation FOS: Mathematics Discrete Mathematics and Combinatorics System order reduction Optimal projection equations Mathematics - Numerical Analysis 0101 mathematics Mathematics - Dynamical Systems Mathematics Reduction strategy Numerical Analysis Algebra and Number Theory Model reduction Iterative solves 34C20 41A05 65F10 Numerical Analysis (math.NA) Petrov–Galerkin Norm (mathematics) Geometry and Topology |
| Zdroj: | Linear Algebra and its Applications. 436(8):2916-2943 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2011.07.015 |
| Popis: | We investigate the use of inexact solves for interpolatory model reduction and consider associated perturbation effects on the underlying model reduction problem. We give bounds on system perturbations induced by inexact solves and relate this to termination criteria for iterative solution methods. We show that when a Petrov-Galerkin framework is employed for the inexact solves, the associated reduced order model is an exact interpolatory model for a nearby full-order system; thus demonstrating backward stability. We also give evidence that for $\h2$-optimal interpolation points, interpolatory model reduction is robust with respect to perturbations due to inexact solves. Finally, we demonstrate the effecitveness of direct use of inexact solves in optimal ${\mathcal H}_2$ approximation. The result is an effective model reduction strategy that is applicable in realistically large-scale settings. Comment: 42 pages, 5 figures |
| Databáze: | OpenAIRE |
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