Optimal Monte Carlo Methods for L²-Approximation

2017/05/12 by David Krieg, Krieg, David · 1 citation
Mathematics · #41A25 #41A63 #65C05 #65D15 #65D30 #65Y20 #68Q25 #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1705.04567

openalex publication_date 2017/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct Monte Carlo methods for the L²-approximation in Hilbert spaces of multivariate functions sampling no more than n function values of the target function. Their errors catch up with the rate of convergence and the preasymptotic behavior of the error of any algorithm sampling n pieces of arbitrary linear information, including function values.

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• Universal L₂-approximation using median lattice algorithms

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