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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Using Different Interval Extensions to Increase the Accuracy of the Exact Solution on Recursive Functions

Discontinuity, Nonlinearity, and Complexity 7(2) (2018) 165--172 | DOI:10.5890/DNC.2018.06.005

H. M. Rodrigues Junior; M. L. C. Peixoto; M. E.G. Nepomuceno.; S.A.M. Martins

Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São João del-Rei, MG, 36307-352, Brazil

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The results obtained by numerical computation are not always precise. It happens because a computer has storage limitations and its set of numbers is finite. In this work, the interval analysis is used to give bounds around exact solution of the logistic map function. The connection between computer and interval mathematics makes possible to solve problems that can not be solved efficiently using floating point arithmetic. We use the intersection of different pseudo-orbits obtained by interval extensions to reduce the bounds of the exact solution. The method is applied using the Intlab toolbox. Without any substantial computational effort, we show a reduction of up to 26% in the width of interval by applying the method proposed in this paper.


We would like to thank CAPES, CNPq/INERGE, FAPEMIG and Federal University of São João del-Rei by support.


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