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

@article{Rauhut2017CompressiveSP,
  title={Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations},
  author={Holger Rauhut and Christoph Schwab},
  journal={Math. Comput.},
  year={2017},
  volume={86},
  pages={661-700}
}
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… CONTINUE READING