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The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the vector of parameters.
Nonlinear approximation
R. DeVore · 1998
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The volume of convex bodies and Banach space geometry
G. Pisier · 1999
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An “hp” certified reduced basis method for parametrized elliptic partial differential equations
J.L. Eftang, A.T. Patera, and E.M. Rønquist · 2010
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Convergence rates for greedy algorithms in reduced basis methods
P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk · 2011
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Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
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Greedy algorithms for reduced bases in Banach spaces
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Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
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Data assimilation in reduced modeling
P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk · 2017
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Reduced basis greedy selection using random training sets
A. Cohen, W. Dahmnen, R. DeVore, and J. Nichols · 2018
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Multivariate approximation in downward closed polynomial spaces
A. Cohen and G. Migliorati · 2018
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Polynomial approximation of anisotropic analytic functions of several variables
A. Bonito, R. DeVore, D. Guignard, P. Jantsch, and G. Petrova · 2019
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An adaptive local reduced basis method for solving PDEs with uncertain inputs and evaluating risk
Z. Zou, D. Kouri, and W. Aquino · 2019
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