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arXiv · 1308.4217

A Geometrical Root Finding Method for Polynomials, with Complexity Analysis

Juan Luis García Zapata·Juan Carlos Díaz Martín
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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.

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Juan Luis García Zapata, Juan Carlos Díaz Martín. 2013-08-20. A Geometrical Root Finding Method for Polynomials, with Complexity Analysis. https://arxiv.org/abs/1308.4217

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