MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Abdul Lateef Haji Ali, Fabio Nobile, Raúl Tempone & Sören Wolfers
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a...
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