Monte Carlo complexity of parametric integration
type: Item
instance of: scholarly article
title: Monte Carlo complexity of parametric integration
zbMATH Open document ID: 0958.68068
author: Stefan Heinrich
author: Eugène Sindambiwe
published in: Journal of Complexity
publication date: 2001-04-01T00:00:00Z
review text: This article is an application of Monte Carlo methods to perform multivariate integration. Usually, Monte Carlo methods are used to approximate single integrals. Goal of this article is to study the case of parametric integration, that is cases where the integrad depends on a parameter. An open research field is the complexity analysis of parametric integration. This paper consider the complexity of computing integrals depending on a parameter for smooth integrands. An optimal algorithm is developed on the basis of a multigrid variance reduction technique. The complexity analysis implies that the algorithm attains a higher convergence rate than any deterministic algorithm. Because of savings due to computation on multiple grids, this rate is also higher than that of previously developed Monte Carlo algorithms for parametrics integration.
reviewed by: Giovanni Cesari
Mathematics Subject Classification ID: 68Q15
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1389252
zbMATH Keywords: Monte Carlo
zbMATH Keywords: parametric integration
MaRDI profile type: Publication
full work available at URL: jcom.1999.0508
OpenAlex ID: W2050871708
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DOI: 10.1006/JCOM.1999.0508
description: scientific article; zbMATH DE number 1389252