Dynamical analysis on cubic polynomials of Damped Traub’s method for approximating multiple roots

Dynamical analysis on cubic polynomials of Damped Traub’s method for approximating multiple roots In this paper, the performance of a parametric family including Newton’s and Traub’s schemes on multiple roots is analyzed. The local order of convergence on nonlinear equations with multiple roots is studied as well as the dynamical behavior in terms of the damping parameter on cubic polynomials with multiple roots. The fixed and critical points, and the associated parameter plane are some of the characteristic dynamical features of the family which are obtained in this work. From the analysis of these elements we identify members of the family of methods with good numerical properties in terms of stability and efficiency both for finding the simple and multiple roots, and also other ones with very unstable behavior. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

Dynamical analysis on cubic polynomials of Damped Traub’s method for approximating multiple roots

Applied Mathematics and Computation, Volume 328 – Jul 1, 2018
18 pages

/lp/elsevier/dynamical-analysis-on-cubic-polynomials-of-damped-traub-s-method-for-43u0JeDFNb
Publisher
Elsevier
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.043
Publisher site
See Article on Publisher Site

Abstract

In this paper, the performance of a parametric family including Newton’s and Traub’s schemes on multiple roots is analyzed. The local order of convergence on nonlinear equations with multiple roots is studied as well as the dynamical behavior in terms of the damping parameter on cubic polynomials with multiple roots. The fixed and critical points, and the associated parameter plane are some of the characteristic dynamical features of the family which are obtained in this work. From the analysis of these elements we identify members of the family of methods with good numerical properties in terms of stability and efficiency both for finding the simple and multiple roots, and also other ones with very unstable behavior.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 1, 2018

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