English

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.

Keywords

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

R2 v1 2026-06-21T20:29:45.914Z