Automatic, guaranteed integration of analytic functions
type: Item
instance of: scholarly article
title: Automatic, guaranteed integration of analytic functions
zbMATH Open document ID: 0688.65017
DOI: 10.1007/BF01952682
author: M. C. Eiermann
published in: BIT
publication date: 1989-01-01T00:00:00Z
review text: Combining the method to compute the bounds for homogeneous functional L on the set of analytic functions, which was developed by \textit{P. Davis} [J. Rat. Mech. Analysis 2, 303-313 (1953; Zbl 0050.130)], and ideas on using interval arithmetic, in particular the arithmetic operations on the set of complex circles, the author gives rigorous error bounds for numerical integration of analytic functions. After this, he develops a strategy to integrate numerically these functions. The strategy consists of the way how the interval of integration must be broken up into subintervals and then choosing the order of numerical integration formula used over each subinterval. Interval analysis and the aforementioned estimates are used to propose a program of automatic integration of analytic function with guaranteed accurracy. There are a discussion of the program, its possibilities, and three numerical examples.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 4128289
zbMATH Keywords: rigorous error bounds
zbMATH Keywords: numerical integration of analytic functions
zbMATH Keywords: Interval analysis
zbMATH Keywords: automatic integration
zbMATH Keywords: guaranteed accurracy
zbMATH Keywords: numerical examples
reviewed by: Leonid Lebedev
describes a project that uses: QUADPACK
MaRDI profile type: Publication
cites work: Adaptive, Self-Validating Numerical Quadrature
cites work: Q5817797
cites work: On the Estimation of Quadrature Errors for Analytic Functions
cites work: Über ableitungsfreie Schranken für Quadraturfehler
cites work: Q4746719
cites work: A Metalgorithm for Adaptive Quadrature
full work available at URL: https://doi.org/10.1007/bf01952682
OpenAlex ID: W2085215060
description: scientific article; zbMATH DE number 4128289