Cubic convergence of parameter-controlled Newton-secant method for multiple zeros

DOI10.1016/j.cam.2009.08.054zbMath1194.65073OpenAlexW2031674139MaRDI QIDQ1034649

Young Ik Kim, Young Hee Geum

Publication date: 6 November 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.08.054

zbMATH Keywords

convergencenumerical examplesasymptotic errorsecant methodmultiple zeroleap-frogging Newton's methodparameter-controlled

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Numerical computation of roots of polynomial equations (65H04)

Related Items (12)

A general family of third order method for finding multiple roots ⋮ Comparative study of methods of various orders for finding repeated roots of nonlinear equations ⋮ On constructing two-point optimal fourth-order multiple-root finders with a generic error corrector and illustrating their dynamics ⋮ A family of optimal quartic-order multiple-zero finders with a weight function of the principal \(k\)th root of a derivative-to-derivative ratio and their basins of attraction ⋮ A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points ⋮ Comparing the basins of attraction for Kanwar-Bhatia-Kansal family to the best fourth order method ⋮ Basins of attraction for several third order methods to find multiple roots of nonlinear equations ⋮ A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics ⋮ Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points ⋮ The dynamical analysis of a uniparametric family of three-point optimal eighth-order multiple-root finders under the Möbius conjugacy map on the Riemann sphere ⋮ On the optimality of some multi-point methods for finding multiple roots of nonlinear equation ⋮ A new biparametric family of two-point optimal fourth-order multiple-root finders

Uses Software

• Mathematica

Cites Work

• A third-order modification of Newton method for systems of non-linear equations
• A third-order Newton type method for nonlinear equations based on modified homotopy perturbation method
• The asymptotic error constant of leap-frogging Newton's method locating a simple real zero
• On the construction of iterative methods with at least cubic convergence
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