Quadratic interval refinement for real roots-Reference-Cited by-同舟云学术

Quadratic interval refinement for real roots

Published:2014-07-10 Issue:1/2 Volume:48 Page:3-12
ISSN:1932-2240
Container-title:ACM Communications in Computer Algebra
language:en
Short-container-title:ACM Commun. Comput. Algebra

Author:

Abbott John¹

Affiliation:

1. Università di Genova, Genova, Italy

Abstract

We present a new algorithm for refining a real interval containing a single real root: the new method combines the robustness of the classical Bisection algorithm with the speed of the Newton-Raphson method; that is, 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-Raphson our method does not need to evaluate the derivative.

Publisher

Association for Computing Machinery (ACM)

Link

https://dl.acm.org/doi/pdf/10.1145/2644288.2644291

Reference12 articles.

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