Interval Newton Iteration in Multiple Precision for the Univariate Case
Résumé
In this paper, interval arithmetic using an underlying multiple precision arithmetic is briefly presented. Then interval Newton iteration for solving nonlinear equations is introduced. A new Newton's algorithm based on multiple precision interval arithmetic is given, along with its properties: termination- , arbitrary accuracy on the computed zeros, automatic and dynamic adaptation of the precision. Finally some experiments illustrate the behaviour of this method.