33 citations · 62 across the 26 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…
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…
Iterative Methods Based on Soft Thresholding of Hierarchical Tensors
Markus Bachmayr, Reinhold Schneider
We construct a soft thresholding operation for rank reduction of hierarchical tensors and subsequently consider its use in iterative thresholding methods, in particular for the sol…