323 citations · 346 across the 14 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^…
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…
Approximation of high-dimensional parametric PDEs
Albert Cohen, Ronald Devore
Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applic…
Kolmogorov widths under holomorphic mappings
Albert Cohen, Ronald Devore
If is a bounded linear operator mapping the Banach space into the Banach space and is a compact set in , then the Kolmogorov widths of the image do not ex…