Probabilistic analysis of numerical integration algorithms
type: Item
instance of: scholarly article
title: Probabilistic analysis of numerical integration algorithms
zbMATH Open document ID: 0724.65020
DOI: 10.1016/0885-064X(91)90044-X
author: D. Kharzeev
published in: Journal of Complexity
publication date: 1991-01-01T00:00:00Z
review text: The author studies the expected error of approximation for a class of adaptive numerical integration methods. He analyzes a heuristic error criterion that can be used to choose the initial approximation and serve as the termination and adaptation criterion with a rigorous mathematical (probabilistic) basis. The probabilistic model assumes that the functions are distributed according to a k-fold Wiener measure on an appropriate space of k-times continuously differentiable functions.
reviewed by: Willy J. F. Govaerts
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 4195025
zbMATH Keywords: error estimation
zbMATH Keywords: adaptive numerical integration
zbMATH Keywords: probabilistic model
zbMATH Keywords: Wiener measure
MaRDI profile type: Publication
cites work: Q5533688
cites work: Q3223667
cites work: A probabilistic theory for error estimation in automatic integration
cites work: Gaussian measures in Banach spaces
cites work: Q4113353
cites work: On the Power of Adaptive Information for Functions with Singularities
full work available at URL: 0885-064x(91)90044-x
OpenAlex ID: W1967176776
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description: scientific article; zbMATH DE number 4195025