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Chkifa, Abdellah; Cohen, Albert; Migliorati, Giovanni; Nobile, Fabio; Tempone, Raul

Discrete least squares polynomial approximation with random evaluations - application to parametric and stochastic elliptic PDEs. (English) Zbl 1318.41004

ESAIM, Math. Model. Numer. Anal. 49, No. 3, 815-837 (2015).
The authors analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Here they discuss the quasi-optimality of the polynomial least-squares method in arbitrary dimension. The optimality criterion only involves the relation between the number of samples and the dimension of the polynomial space, independently of the anisotropic shape and of the number of variables.
Reviewer: Vijay Gupta (New Delhi)

Cited in 2 Reviews
Cited in 50 Documents

MSC:

41A10 Approximation by polynomials
41A35 Approximation by operators (in particular, by integral operators)

Keywords:

approximation theory; polynomial approximation; least squares; parametric and stochastic PDEs; highdimensional approximation
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References:

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