Geodesic
Convergence Rates of the POD-Greedy Method
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 3, pp. 859-873

Voir la notice de l'article provenant de la source Numdam

MR Zbl

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.

DOI : 10.1051/m2an/2012045
Classification : 65D15, 35B30, 58B99, 37C50
Keywords: greedy approximation, proper orthogonal decomposition, convergence rates, reduced basis methods 
Haasdonk, Bernard. Convergence Rates of the POD-Greedy Method. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 3, pp. 859-873. doi: 10.1051/m2an/2012045
@article{M2AN_2013__47_3_859_0,
     author = {Haasdonk, Bernard},
     title = {Convergence {Rates} of the {POD-Greedy} {Method}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {859--873},
     year = {2013},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {3},
     doi = {10.1051/m2an/2012045},
     mrnumber = {3056412},
     zbl = {1277.65074},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012045/}
}
TY  - JOUR
AU  - Haasdonk, Bernard
TI  - Convergence Rates of the POD-Greedy Method
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2013
SP  - 859
EP  - 873
VL  - 47
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012045/
DO  - 10.1051/m2an/2012045
LA  - en
ID  - M2AN_2013__47_3_859_0
ER  - 
%0 Journal Article
%A Haasdonk, Bernard
%T Convergence Rates of the POD-Greedy Method
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2013
%P 859-873
%V 47
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012045/
%R 10.1051/m2an/2012045
%G en
%F M2AN_2013__47_3_859_0

Cité par Sources :