JUCS - Journal of Universal Computer Science 26(10): 1312-1330, doi: 10.3897/jucs.2020.068
Interval Methods for Fixed and Periodic Points: Development and Visualization
expand article infoJosé Eduardo de Almeida Ayres‡, Luiz Henrique Henrique de Figueiredo
‡ IMPA, Rio de Janeiro, Brazil

Corresponding author: José Eduardo de Almeida Ayres ( jeaayres@impa.br )

© José Eduardo de Almeida Ayres, Luiz Henrique de Figueiredo.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY-ND 4.0). This license allows reusers to copy and distribute the material in any medium or format in unadapted form only, and only so long as attribution is given to the creator. The license allows for commercial use.
Citation: Ayres JEA, de Figueiredo LHH (2020) Interval Methods for Fixed and Periodic Points: Development and Visualization. JUCS - Journal of Universal Computer Science 26(10): 1312-1330. https://doi.org/10.3897/jucs.2020.068
Open Access
Abstract
We describe the development of rigorous numerical methods based on interval analysis for finding all fixed points of a map and all attracting periodic points of a complex polynomial. We also discuss their performance with instructive visualizations.
Keywords
fixed points, interval analysis, computer-assisted proofs