Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

@article{Nobile2016ConvergenceOQ,
  title={Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs},
  author={Fabio Nobile and Lorenzo Tamellini and Ra{\'u}l Tempone},
  journal={Numerische Mathematik},
  year={2016},
  volume={134},
  pages={343-388}
}
In this work we provide a convergence analysis for the quasi-optimal version of the Stochastic Sparse Grid Collocation method we had presented in our previous work “On the optimal polynomial approximation of Stochastic PDEs by Galerkin and Collocation methods” [6]. Here the construction of a sparse grid is recast into a knapsack problem: a profit is assigned to each hierarchical surplus and only the most profitable ones are added to the sparse grid. The convergence rate of the sparse grid… CONTINUE READING
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