A modification of the classical quadrature method for locating zeros of analytic functions
type: Item
instance of: scholarly article
title: A modification of the classical quadrature method for locating zeros of analytic functions
zbMATH Open document ID: 0604.65024
DOI: 10.1007/BF01936146
author: B. George
published in: BIT
publication date: 1985-01-01T00:00:00Z
review text: The classical method for determination of a simple zero a of an analytic function f(z) inside a closed contour C by using the formula \(a=(2\pi i)^{-1}\int_{c}[zf'(z)/f(z)]dz\) is reconsidered and modified. The modification consists in using the Cauchy theorem instead of the Cauchy formula and, further, evaluating numerically a as one of the zeros of an appropriate polynomial depending on the quadrature rule used. The case of circular contours with application of the trapezoidal rule is considered in detail and numerical results are presented.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 3976210
zbMATH Keywords: simple zero
zbMATH Keywords: analytic function
zbMATH Keywords: Cauchy theorem
zbMATH Keywords: quadrature rule
zbMATH Keywords: trapezoidal rule
zbMATH Keywords: numerical results
MaRDI profile type: Publication
cites work: Q3323133
cites work: A Numerical Method for Locating the Zeros of an Analytic Function
cites work: Numerical Evaluation of Integrals Around Simple Closed Curves
cites work: Q5653524
cites work: On Numerical Contour Integration Round a Closed Contour
cites work: Exact Inversion of Dispersion Relations
description: scientific article; zbMATH DE number 3976210