Fast Root-finding of Nonlinear Equations in Geometric Computation
- https://doi.org/10.2991/iccia.2012.319How to use a DOI?
- Newton’s method, Convergence order, Divided difference, Non-linear equation
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.
- © 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/).
Cite this article
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 - https://doi.org/10.2991/iccia.2012.319 ID - Geng2014/05 ER -