Optimal Monte Carlo Methods for L2 -Approximation

David Krieg

doi:10.1007/s00365-018-9428-4

Optimal Monte Carlo Methods for L2 -Approximation

David Krieg

Research output: Contribution to journal › Article › peer-review

Abstract

We construct Monte Carlo methods for the L2-approximation in Hilbert spaces of multivariate functions sampling not 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.

Original language	English
Pages (from-to)	385-403
Number of pages	19
Journal	Constructive Approximation
Volume	49
Issue number	2
DOIs	https://doi.org/10.1007/s00365-018-9428-4
Publication status	Published - 15 Apr 2019

Fields of science

101002 Analysis
101032 Functional analysis

JKU Focus areas

Digital Transformation

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10.1007/s00365-018-9428-4

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abstract = "We construct Monte Carlo methods for the L2-approximation in Hilbert spaces of multivariate functions sampling not 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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JO - Constructive Approximation

JF - Constructive Approximation

IS - 2

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Optimal Monte Carlo Methods for L2 -Approximation

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