Quadratic Interval Refinement for Real Roots
Numerical Analysis
2014-07-01 v1
Abstract
We present a new algorithm for refining a real interval containing a single real root: the new method combines characteristics of the classical Bisection algorithm and Newton's Iteration. Our method exhibits quadratic convergence when refining isolating intervals of simple roots of polynomials (and other well-behaved functions). We assume the use of arbitrary precision rational arithmetic. Unlike Newton's Iteration our method does not need to evaluate the derivative.
Cite
@article{arxiv.1203.1227,
title = {Quadratic Interval Refinement for Real Roots},
author = {John Abbott},
journal= {arXiv preprint arXiv:1203.1227},
year = {2014}
}
Comments
Originally presented as a "Poster" at ISSAC 2006