When Newton meets Descartes: a simple and fast algorithm to isolate the real roots of a polynomial

@inproceedings{Sagraloff2012WhenNM,
title={When Newton meets Descartes: a simple and fast algorithm to isolate the real roots of a polynomial},
author={Michael Sagraloff},
booktitle={ISSAC},
year={2012}
}
We introduce a novel algorithm denoted NewDsc to isolate the real roots of a univariate square-free polynomial f with integer coefficients. The algorithm iteratively subdivides an initial interval which is known to contain all real roots of f and performs exact (rational) operations on the coefficients of f in each step. For the subdivision strategy, we combine Descartes' Rule of Signs and Newton iteration. More precisely, instead of using a fixed subdivision strategy such as bisection in each…
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