Optimal weighted least-squares methods

• Published in: SMAI Journal of Computational Mathematics Vol. 3; pp. 181 - 203
• Main Authors: Cohen, Albert, Migliorati, Giovanni
• Format: Journal Article
• Language: English
• Published: Société de Mathématiques Appliquées et Industrielles (SMAI) 2017
• Subjects: Mathematics; Numerical Analysis; ran-dom matrices; error analysis; weighted least squares; polynomial approximation Math classification 41A10; multivariate approximation; convergence rates; conditional sampling

We consider the problem of reconstructing an unknown bounded function u defined on a domain X ⊂ R d from noiseless or noisy samples of u at n points (x i)i=1,...,n. We measure the reconstruction error in a norm L 2 (X, dρ) for some given probability measure dρ. Given a linear space Vm with dim(Vm) =...