# A priori convergence of the Greedy algorithm for the parametrized reduced basis method

Annalisa Buffa; Yvon Maday; Anthony T. Patera; Christophe Prud’homme; Gabriel Turinici

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 3, page 595-603
- ISSN: 0764-583X

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topBuffa, Annalisa, et al. "A priori convergence of the Greedy algorithm for the parametrized reduced basis method." ESAIM: Mathematical Modelling and Numerical Analysis 46.3 (2012): 595-603. <http://eudml.org/doc/277851>.

@article{Buffa2012,

abstract = {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.},

author = {Buffa, Annalisa, Maday, Yvon, Patera, Anthony T., Prud’homme, Christophe, Turinici, Gabriel},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Greedy algorithm; reduced basis approximations; a priori analysis; best fit analysis; greedy algorithm; a priori error bounds; Galerkin method; convergence},

language = {eng},

month = {1},

number = {3},

pages = {595-603},

publisher = {EDP Sciences},

title = {A priori convergence of the Greedy algorithm for the parametrized reduced basis method},

url = {http://eudml.org/doc/277851},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Buffa, Annalisa

AU - Maday, Yvon

AU - Patera, Anthony T.

AU - Prud’homme, Christophe

AU - Turinici, Gabriel

TI - A priori convergence of the Greedy algorithm for the parametrized reduced basis method

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2012/1//

PB - EDP Sciences

VL - 46

IS - 3

SP - 595

EP - 603

AB - 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.

LA - eng

KW - Greedy algorithm; reduced basis approximations; a priori analysis; best fit analysis; greedy algorithm; a priori error bounds; Galerkin method; convergence

UR - http://eudml.org/doc/277851

ER -

## References

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## Citations in EuDML Documents

top- Abdellah Chkifa, Albert Cohen, Ronald DeVore, Christoph Schwab, Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
- D. Chapelle, A. Gariah, P. Moireau, J. Sainte-Marie, A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation

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