A priori convergence of the greedy algorithm for the parametrized reduced basis method
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 3, p. 595-603

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that three greedy algorithms converge; the last algorithm, based on the use of an a posteriori estimator, is the approach actually employed in the calculations.

DOI : https://doi.org/10.1051/m2an/2011056
Classification:  41A45,  41A65,  65N15
Keywords: greedy algorithm, reduced basis approximations, a priori analysis, best fit analysis
@article{M2AN_2012__46_3_595_0,
     author = {Buffa, Annalisa and Maday, Yvon and Patera, Anthony T. and Prud'homme, Christophe and Turinici, Gabriel},
     title = {A priori convergence of the greedy algorithm for the parametrized reduced basis method},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {3},
     year = {2012},
     pages = {595-603},
     doi = {10.1051/m2an/2011056},
     zbl = {1272.65084},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2012__46_3_595_0}
}
Buffa, Annalisa; Maday, Yvon; Patera, Anthony T.; Prud’homme, Christophe; Turinici, Gabriel. A priori convergence of the greedy algorithm for the parametrized reduced basis method. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 3, pp. 595-603. doi : 10.1051/m2an/2011056. http://www.numdam.org/item/M2AN_2012__46_3_595_0/

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