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Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations

2016
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Mathematics of Computation
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We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly infinitely many parameters. The proposed algorithms are based on so-called "non-intrusive" sampling of the high-dimensional parameter space, reminiscent of Monte-Carlo sampling. In contrast to Monte-Carlo, however, the parametric solution is then computed via

doi:10.1090/mcom/3113
fatcat:ssuu6iyc3bdtngp6hgk4xajc5i