Automatic quadrature of functions of the form \(g(| f(x)|)\)
type: Item
instance of: scholarly article
title: Automatic quadrature of functions of the form \(g(| f(x)|)\)
zbMATH Open document ID: 0853.65030
DOI: 10.1007/BF01731990
author: Antoinetta Venter
author: Dirk Laurie
published in: BIT
publication date: 1996-06-09T00:00:00Z
review text: This paper provides a description for an interesting and useful modification to adaptive integration methods when applied to integrands of the form \(g(|f(x)|)\), for smooth functions \(f(x)\) and \(g(x)\). The key idea is to use signs of the \(f(x)\) values that are computed during the adaptivity and integral estimation process, for standard adaptive integration algorithms, to detect the presence of zeros within the integration interval. When a sign change is found, a little extra work is used to accurately locate a zero of the integrand, and these zeros are used for interval subdivision points as the algorithm continues. Test results from a battery of examples are used by the authors to illustrate how software using this approach can be more efficient than standard software.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 885560
zbMATH Keywords: automatic quadrature
zbMATH Keywords: numerical examples
zbMATH Keywords: adaptive integration methods
zbMATH Keywords: zeros
zbMATH Keywords: subdivision
reviewed by: A. Genz
describes a project that uses: QUADPACK
MaRDI profile type: Publication
cites work: On the subdivision strategy in adaptive quadrature algorithms
cites work: Q5595535
cites work: Q4746721
cites work: Q5533728
cites work: Q5679602
cites work: Q3323133
cites work: Q3881787
description: scientific article; zbMATH DE number 885560