# Quadrature Methods for the Determination of Zeros of Transcendental Functions - A Review

@inproceedings{Ioakimidis1987QuadratureMF, title={Quadrature Methods for the Determination of Zeros of Transcendental Functions - A Review}, author={Nikolaos I. Ioakimidis}, year={1987} }

A review of quadrature methods for the numerical determination of zeros of algebraic or transcendental functions is presented. Most of these methods are based on the classical theory of analytic functions, but, recently, relevant methods based on the elementary theory of real functions were also developed. On the other hand, purely numerical methods were also recently proposed. The common point of these methods is the use of numerical integration rules for the determination of the…

## 33 Citations

Location of essential singularities of a class of analytic functions

- Mathematics
- 1988

A simple method, based on the numerical evaluation of appropriate complex integrals on a closed contour by using appropriate numerical integration rules, is proposed for the location of essential…

Error Analysis of a Derivative-Free Algorithm for Computing Zeros of Holomorphic Functions

- MathematicsComputing
- 2003

The quadrature method developed by Kravanja and Van Barel for computing all the zeros of a holomorphic function that lie inside the unit circle is considered and the resulting quadratures error is investigated.

A method for locating the zeros of analytic functions in the unit circle

- Mathematics
- 2001

Delves and Lyness [1] proposed a method to compute ζ1, . . . , ζn using the integrals (1). Methods for the determination of zeros of analytic functions that are based on the numerical evaluation of…

An error analysis of two related quadrature methods for computing zeros of analytic functions

- Mathematics
- 2003

On Locating Clusters of Zeros of Analytic Functions

- Mathematics
- 1999

Given an analytic function f and a Jordan curve γ that does not pass through any zero of f, we consider the problem of computing all the zeros of f that lie inside γ, together with their respective…

Locating branch points of sectionally analytic functions by using contour integrals and numerical integration rules

- MathematicsInt. J. Comput. Math.
- 1992

The classical method for locating zeros (and/or poles) of analytic functions in the complex plane on the basis of appropriate complex contour integrals is shown to be applicable to the location of branch points of sectionally analytic functions.

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