Quadratic Interval Refinement for Real Roots

Description

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.

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