Integration of monotone functions of several variables
type: Item
instance of: scholarly article
title: Integration of monotone functions of several variables
zbMATH Open document ID: 0780.65015
author: K. Appert
published in: Journal of Complexity
publication date: 1993-08-24T00:00:00Z
review text: The author studies the approximation of integrals of monotone functions of \(d\) variables. For this purpose he presents algorithms that use evaluations taken at \(n\) points of \([0,1]^ d\) and which approximate the integral \(\int_{[0,1]^ d}f(x)dx\) with minimal error. He shows the following facts: (1) the minimal worst case error is \(O(n^{-1/d})\); (2) the minimal error of randomized methods is \(O(n^{- 1/2-1/d})\); (3) the complexity of approximating integrals of monotone functions with error at most \(\varepsilon\) is \(O(\varepsilon^{-d})\) in the worst case and \(O(\varepsilon^{-2(1+2/d)})\) in the randomized case.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 370453
zbMATH Keywords: Monte Carlo methods
zbMATH Keywords: integrals of monotone functions
zbMATH Keywords: minimal worst case error
zbMATH Keywords: randomized methods
zbMATH Keywords: complexity
reviewed by: Dumitru Acu
MaRDI profile type: Publication
full work available at URL: jcom.1993.1017
OpenAlex ID: W2012372674
DOI: 10.1006/JCOM.1993.1017
description: scientific article; zbMATH DE number 370453