# Convergence Rates of the POD–Greedy Method

- Volume: 47, Issue: 3, page 859-873
- ISSN: 0764-583X

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topHaasdonk, Bernard. "Convergence Rates of the POD–Greedy Method." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.3 (2013): 859-873. <http://eudml.org/doc/273114>.

@article{Haasdonk2013,

abstract = {Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy algorithm (Haasdonk and Ohlberger 2008). In this algorithm, each greedy step is invoking a temporal compression step by performing a proper orthogonal decomposition (POD). Using a suitable coefficient representation of the POD–Greedy algorithm, we show that the existing convergence rate results of the Greedy algorithm can be extended. In particular, exponential or algebraic convergence rates of the Kolmogorov n-widths are maintained by the POD–Greedy algorithm.},

author = {Haasdonk, Bernard},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {greedy approximation; proper orthogonal decomposition; convergence rates; reduced basis methods; convergence; algorithm},

language = {eng},

number = {3},

pages = {859-873},

publisher = {EDP-Sciences},

title = {Convergence Rates of the POD–Greedy Method},

url = {http://eudml.org/doc/273114},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Haasdonk, Bernard

TI - Convergence Rates of the POD–Greedy Method

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 3

SP - 859

EP - 873

AB - Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy algorithm (Haasdonk and Ohlberger 2008). In this algorithm, each greedy step is invoking a temporal compression step by performing a proper orthogonal decomposition (POD). Using a suitable coefficient representation of the POD–Greedy algorithm, we show that the existing convergence rate results of the Greedy algorithm can be extended. In particular, exponential or algebraic convergence rates of the Kolmogorov n-widths are maintained by the POD–Greedy algorithm.

LA - eng

KW - greedy approximation; proper orthogonal decomposition; convergence rates; reduced basis methods; convergence; algorithm

UR - http://eudml.org/doc/273114

ER -

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## Citations in EuDML Documents

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