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.

Quadratic Interval Refinement for Real Roots

ABBOTT, JOHN ANTHONY
2014

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/764191
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