Weierstrass formula and zero-finding methods

DOI10.1007/s002110050097zbMath0821.65028OpenAlexW2153196903WikidataQ29026800 ScholiaQ29026800MaRDI QIDQ1347051

Miroslav Trajkovíc, Miodrag S. Petković, Carsten Carstensen

Publication date: 27 September 1995

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002110050097

zbMATH Keywords

stabilitynumerical examplesiterative methodquadratic convergenceinterval arithmeticanalytic functionsinclusion methodscircular complex arithmeticzero-finding methodsinclusion diskslocalization of polynomial zerosWeierstrass' formula

Mathematics Subject Classification ID

Related Items (35)

On the guaranteed convergence of the fourth order simultaneous method for polynomial zeros ⋮ Point estimation of simultaneous methods for solving polynomial equations: A survey. II. ⋮ A posteriori error bound methods for the inclusion of polynomial zeros ⋮ The behaviour of approximations of the SOR Weierstrass method ⋮ On the guaranteed convergence of the square-root iteration method ⋮ The guaranteed convergence of Laguerre-like method ⋮ Polynomial root finding by means of continuation ⋮ Tchebychef-like method for the simultaneous finding zeros of analytic functions ⋮ A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously ⋮ On some simultaneous methods based on Weierstrass' correction ⋮ On initial conditions for the convergence of simultaneous root finding methods ⋮ On Euler-like methods for the simultaneous approximation of polynomial zeros ⋮ On parallel complexity of analytic functions ⋮ Point estimation and some applications to iterative methods ⋮ Relationships between different types of initial conditions for simultaneous root finding methods ⋮ New higher-order methods for the simultaneous inclusion of polynomial zeros ⋮ A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously ⋮ On the convergence condition of generalized root iterations for the inclusion of polynomial zeros ⋮ High order Euler-like method for the inclusion of polynomial zeros ⋮ Extracting \(S\)-matrix poles for resonances from numerical scattering data: type-II Padé reconstruction ⋮ Efficient methods for the inclusion of polynomial zeros ⋮ Approximate Calculation of Sums II: Gaussian Type Quadrature ⋮ The convergence of a family of parallel zero-finding methods ⋮ A new fourth-order family of simultaneous methods for finding polynomial zeros ⋮ Point estimation of simultaneous methods for solving polynomial equations: A survey ⋮ A higher order family for the simultaneous inclusion of multiple zeros of polynomials ⋮ General convergence theorems for iterative processes and applications to the Weierstrass root-finding method ⋮ On the guaranteed convergence of new two-point root-finding methods for polynomial zeros ⋮ Point estimation of a family of simultaneous zero-finding methods ⋮ The Weierstrass iterative method as a Petrov-Galerkin method for solving eigenvalue problem ⋮ The convergence of Euler-like method for the simultaneous inclusion of polynomial zeros ⋮ On the guaranteed convergence of a cubically convergent Weierstrass-like root-finding method ⋮ On the convergence of Wang-Zheng's method ⋮ Improvement of a convergence condition for Durand-Kerner iteration ⋮ Improved Halley-like methods for the inclusion of polynomial zeros

This page was built for publication: Weierstrass formula and zero-finding methods