Detecting unreliable computer simulations of recursive functions with interval extensions

Detecting unreliable computer simulations of recursive functions with interval extensions This paper presents a procedure to detect unreliable computer simulations of recursive functions. The proposed method calculates a lower bound error which is derived from two different pseudo-orbits based on interval extensions. The interval extensions are generated by taking into account the associative property of multiplication, which keeps the same error bound. We have tested our approach on the logistic map using many different programming languages and simulation packages, including Matlab, Scilab, Octave, Fortran and C. In all cases, the number of iterates is significantly lower than that considered reliable in the existing literature. We have also used the lower bound error on the logistic map and on the polynomial NARMAX for the Rössler equations to estimate the largest Lyapunov exponent, which determines the critical simulation time that guarantees the reliability of the simulation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

Detecting unreliable computer simulations of recursive functions with interval extensions

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.02.020
Publisher site
See Article on Publisher Site

Abstract

This paper presents a procedure to detect unreliable computer simulations of recursive functions. The proposed method calculates a lower bound error which is derived from two different pseudo-orbits based on interval extensions. The interval extensions are generated by taking into account the associative property of multiplication, which keeps the same error bound. We have tested our approach on the logistic map using many different programming languages and simulation packages, including Matlab, Scilab, Octave, Fortran and C. In all cases, the number of iterates is significantly lower than that considered reliable in the existing literature. We have also used the lower bound error on the logistic map and on the polynomial NARMAX for the Rössler equations to estimate the largest Lyapunov exponent, which determines the critical simulation time that guarantees the reliability of the simulation.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

References

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