Quadratic Interval Refinement for Real Roots

Details Quadratic Interval Refinement for Real Roots Quadratic Interval Refinement for Real Roots

2012-03-06

arxiv.org/abs/1203.1227v1

Mathematics

Numerical Analysis

Originally presented as a "Poster" at ISSAC 2006

Scientific paper

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.

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