323 citations · 420 across the 20 of their papers we have counts for
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Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients
Markus Bachmayr, Albert Cohen, Ronald DeVore +1
Elliptic partial differential equations with diffusion coefficients of lognormal form, that is , where is a Gaussian random field, are considered. We study the $\ell^…
Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
Markus Bachmayr, Albert Cohen, Giovanni Migliorati
We consider elliptic partial differential equations with diffusion coefficients that depend affinely on countably many parameters. We study the summability properties of polynomial…
Orthogonal Matching Pursuit under the Restricted Isometry Property
Albert Cohen, Wolfgang Dahmen, Ronald DeVore
This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary in a Hilbert space . Given an elemen…
Data Assimilation in Reduced Modeling
Peter Binev, Albert Cohen, Wolfgang Dahmen +3
We consider the problem of optimal recovery of an element of a Hilbert space from measurements obtained through known linear functionals on . Pro…
Kolmogorov widths and low-rank approximations of parametric elliptic PDEs
Markus Bachmayr, Albert Cohen
Kolmogorov -widths and low-rank approximations are studied for families of elliptic diffusion PDEs parametrized by the diffusion coefficients. The decay of the -widths can be…