Computational complexity of the integration problem for anisotropic classes
type: Item
instance of: scholarly article
title: Computational complexity of the integration problem for anisotropic classes
zbMATH Open document ID: 1071.65030
published in: Advances in Computational Mathematics
publication date: 2005-05-20T00:00:00Z
review text: There is an increasing interest in studying the computational complexity of high-dimensional integration due to its applications in computational mathematics, finance, physics, engineering and in statistics. The author studies this problem in a considerable generality. More precisely, by developing a decomposition technique of Borel measure on the unit cube of a \(d\)-dimensional Euclidean space, he determines the exact order of \(\epsilon\)--complexity of the numerical integration problem for the anisotropic class \(W_\infty^r(I^d)\) and \(H_\infty^r(I^d)\). In addition, by the imbedding relationship between function classes, he extends the results to the classes of functions \(W_p^{\wedge}(I^d)\) and \(H_p^{\wedge}(I^d)\).
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 2170081
zbMATH Keywords: high-dimensional integration
zbMATH Keywords: epsilon complexity
zbMATH Keywords: randomized methods
zbMATH Keywords: anisotropic classes
author: Pei-Xin Ye
reviewed by: Sonia Pérez Díaz
MaRDI profile type: Publication
full work available at URL: s10444-004-1830-8
OpenAlex ID: W106095660
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DOI: 10.1007/S10444-004-1830-8
description: scientific article; zbMATH DE number 2170081