Interval Newton Iteration in Multiple Precision for the Univariate Case

Nathalie Revol 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : 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.
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https://hal.inria.fr/inria-00072253
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Submitted on : Tuesday, May 23, 2006 - 8:14:02 PM
Last modification on : Thursday, February 7, 2019 - 4:47:16 PM
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Nathalie Revol. Interval Newton Iteration in Multiple Precision for the Univariate Case. [Research Report] RR-4334, INRIA. 2001. ⟨inria-00072253⟩

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