Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

@article{Chkifa2015DiscreteLS,
  title={Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs},
  author={Abdellah Chkifa and A. Cohen and G. Migliorati and F. Nobile and R. Tempone},
  journal={Mathematical Modelling and Numerical Analysis},
  year={2015},
  volume={49},
  pages={815-837}
}
Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case, the least-squares method is quasi-optimal in expectation in [A. Cohen, M A. Davenport and D. Leviatan. Found. Comput. Math. 13 (2013) 819–834] and in probability in [G. Migliorati, F. Nobile, E. von Schwerin, R… Expand

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