A Geometrical Root Finding Method for Polynomials, with Complexity Analysis
Numerical Analysis
2013-08-21 v1
Abstract
The usual methods for root finding of polynomials are based on the iteration of a numerical formula for improvement of successive estimations. The unpredictable nature of the iterations prevents to search roots inside a pre-specified region of complex plane. This work describes a root finding method that overcomes this disadvantage. It is based on the winding number of plane curves, a geometric construct that is related to the number of zeros of each polynomial. The method can be restrained to search inside a pre-specified region. It can be easily parallelized. Its correctness is formally proven, and its computational complexity is also analyzed.
Cite
@article{arxiv.1308.4217,
title = {A Geometrical Root Finding Method for Polynomials, with Complexity Analysis},
author = {Juan Luis García Zapata and Juan Carlos Díaz Martín},
journal= {arXiv preprint arXiv:1308.4217},
year = {2013}
}
Comments
56 pages