Fast Root-finding of Nonlinear Equations in Geometric Computation

DOI

10.2991/iccia.2012.319How to use a DOI?

Keywords

Newton’s method, Convergence order, Divided difference, Non-linear equation

Abstract

Computing the roots of polynomials is an important issue in various geometric problems. In this paper, we introduce a new family of iterative methods with sixth and seventh order convergence for nonlinear equations (or polynomials). The new method is obtained by combining a different fourth-order iterative method with Newton’s method and using the approximation based on the divided difference to replace the derivative. It can improve the order of convergence and reduce the required number of functional evaluations per step. Numerical comparisons demonstrate the performance of the presented methods.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Changchun Geng
AU  - Zhong Li
AU  - Tianhe Zhou
AU  - Bin Yang
PY  - 2014/05
DA  - 2014/05
TI  - Fast Root-finding of Nonlinear Equations in Geometric Computation
BT  - Proceedings of the 2012 2nd International Conference on Computer and Information Application (ICCIA 2012)
PB  - Atlantis Press
SP  - 1286
EP  - 1289
SN  - 1951-6851
UR  - https://doi.org/10.2991/iccia.2012.319
DO  - 10.2991/iccia.2012.319
ID  - Geng2014/05
ER  -