Quadratic Interval Refinement

Description

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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