Effectively Subsampled Quadratures for Least Squares Polynomial Approximations

@article{Seshadri2017EffectivelySQ,
  title={Effectively Subsampled Quadratures for Least Squares Polynomial Approximations},
  author={Pranay Seshadri and Akil C. Narayan and Sankaran Mahadevan},
  journal={SIAM/ASA J. Uncertain. Quantification},
  year={2017},
  volume={5},
  pages={1003-1023}
}
This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an existing tensor grid using QR column pivoting. For polynomial interpolation using hyperbolic or total order sets, we then solve the following square least squares problem. For polynomial approximation, we use a column pruning heuristic that removes columns… 
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