David P. Sanders
Department of Physics, Faculty of Sciences, National Autonomous University of Mexico (UNAM), Ciudad Universitaria, México D.F. 04510, Mexico

Luis Benet
Institute of Physical Sciences, National Autonomous University of Mexico (UNAM), Apartado postal 48-3, Cuernavaca 62551, Morelos, Mexico

Abstract

We introduce the ValidiPy package for validated numerics in Python. This suite of tools, which includes interval arithmetic and automatic differentiation, enables rigorous and guaranteed results using floating-point arithmetic. We apply the ValidiPy package to two classic problems in dynamical systems, calculating periodic points of the logistic map, and simulating the dynamics of a chaotic billiard model.

Keywords

validated numerics, Newton method, floating point, interval arithmetic

DOI

10.25080/Majora-14bd3278-00b

Bibtex entry

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Copyright © 2014 David P. Sanders et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.