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Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required.
G. Pisier, The volume of convex bodies and Banach spaces geometry
1989
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Y. Maday, A.T. Patera, and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parametric elliptic partial differential equations
2002
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Y. Maday, A. T. Patera, and G. Turinici, Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations
2002
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A.T. Patera, C. PrudÕhomme, D.V. Rovas, and K. Veroy
2003
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G. Rozza, D.B.P. Huynh, and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations Ñ application to transport and continuum mechanics
2008
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S. Sen, Reduced-basis approximation and a posteriori error estimation for many-parameter heat conduction problems
2008
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P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk, Convergence Rates for Greedy Algorithms in Reduced Basis Methods
2011
Cited alongside, same era.
A. Cohen, R. DeVore, and C. Schwab, Analytic regularity and polynomial approximation of parametric and stochastic PDEs
2011
Cited alongside, same era.
A. Buffa, Y. Maday, A.T. Patera, C. Prud’homme, and G. Turinici, A Priori convergence of the greedy algorithm for the parameterized reduced basis
2012
Cited alongside, same era.
R. DeVore, G. Petrova, and P. Wojtaszczyk, Greedy algorithms for reduced bases in Banach spaces
2013
Cited alongside, same era.
A. Chkifa, A. Cohen, G. Migliorati, F. Nobile and R. Tempone, Discrete least squares polynomial approximation with random evaluations - Application to parametric and stochastic elliptic PDEs
2015
Cited alongside, same era.
A. Chkifa, A. Cohen, and C. Schwab, Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
2015
Later among the works it cites.
A. Cohen and R. DeVore, Approximation of high-dimensional PDEs
2015
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M. Bachmayr, A. Cohen, and G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
2017
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A. Cohen and G. Migliorati, Multivariate approximation in downward closed polynomial spaces
2018
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V. N. Temlyakov,
2018
Closest in time.
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