Journal ArticleDOI
On the simultaneous determination of zeros of analytic or sectionally analytic functions
TLDR
It is shown how the total-step and single-step iterative methods, as well as their improvements, for the simultaneous determination of simple zeros of polynomials can be used for the determination of basic functions or sectionally analytic functions.Abstract:
It is shown how the total-step and single-step iterative methods, as well as their improvements, for the simultaneous determination of simple zeros of polynomials can be used (with one slight modification) for the determination of simple zeros of analytic functions (inside or outside a simple smooth closed contour in the complex plane) or sectionally analytic functions (outside their arcs of discontinuity). Numerical results, obtained by the single-step method, are also presented.read more
Citations
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Journal ArticleDOI
On locating clusters of zeros of analytic functions
TL;DR: In this article, the authors considered the problem of computing all the zeros of an analytic function f and a Jordan curve γ that does not pass through any zero of f, together with their respective multiplicities.
Journal ArticleDOI
Weierstrass formula and zero-finding methods
TL;DR: In this article, the problem of localizing polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros has been investigated and conditions for the safe convergence of Weierstrass' method,depending only on initial approximations are given.
Book ChapterDOI
Quadrature Methods for the Determination of Zeros of Transcendental Functions - A Review
TL;DR: A review of quadrature methods for the numerical determination of zeros of algebraic or transcendental functions is presented, finding the common point of these methods is the use of numerical integration rules for the determination of the aforementioned zeros.
Journal ArticleDOI
All the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox–Wright function: illustration for genome multiplicity in survival of irradiated cells
Dževad Belkić,Dževad Belkić +1 more
TL;DR: In this article, the authors derived a confluent Fox-Wright function for the nth degree trinomial root, which can be expressed as a convex series with binomial expansion coefficients or Pochhammer symbols.
Journal ArticleDOI
Higher-order iterative methods for approximating zeros of analytic functions
TL;DR: The R-order of convergence of the basic total-step and single-step methods, as well as their improvements which use Newton's and Halley's corrections, is given in this paper.
References
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Journal ArticleDOI
Methods of Numerical Integration.
Book ChapterDOI
Riemann boundary value problem
TL;DR: In this article, the Riemann boundary value problem of analytic functions is discussed and the concept of the index of a function is discussed, which is of great value as an auxiliary tool.
Journal ArticleDOI
A Numerical Method for Locating the Zeros of an Analytic Function
L. M. Delves,J. N. Lyness +1 more
Journal ArticleDOI
The use of Riemann problems in solving a class of transcendental equations
E. E. Burniston,C. E. Siewert +1 more
TL;DR: In this article, a method of finding explicit expressions for the roots of a certain class of transcendental equations is discussed, by determining a canonical solution of an associated Riemann boundary-value problem.