Sampling recovery in Bochner spaces and applications to parametric PDEs with random inputs
<|reference_start|>Sampling recovery in Bochner spaces and applications to parametric PDEs with random inputs: We proved convergence rates of linear sampling recovery by extended least squares methods of functions in Bochner space satisfying some $\ell_2$-summability of their generalized polynomial chaos expansion coefficients. As applications we derive convergence rates of linear collocation approximation of solutions to parametric elliptic PDEs with random inputs, and of infinite dimensional holomorphic functions. These convergence rates significantly improve the known results.<|reference_end|>
@article{bartel2024sampling,
    title={Sampling recovery in Bochner spaces and applications to parametric PDEs
  with log-normal random inputs},
    author={Felix Bartel and Dinh D~ung},
    journal={arXiv preprint arXiv:2409.05050},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.05050},
    primaryClass={math.NA cs.NA}
}