TY - JOUR

T1 - Relaxation to the asymptotic distribution of global errors due to round off

AU - Turchetti, G.

AU - Vaienti, S.

AU - Zanlungo, F.

PY - 2010

Y1 - 2010

N2 - We propose an analysis of the effects introduced by finite accuracy and round-off arithmetic on discrete dynamical systems. We investigate, from a statistical viewpoint and using the tool of the decay of fidelity, the error of the numerical orbit with respect to the exact one. As a model we consider a random perturbation of the exact orbit with an additive noise, for which exact results can be obtained for some prototype maps. For regular anysocrounous maps the fidelity has a power law decay, whereas the decay is exponential if a random perturbation is introduced. For chaotic maps the decay is superexponential after an initial plateau and our method is suitable to identify the reliability threshold of numerical results, i.e. a number of iterations below which global errors can be ignored. The same behaviour is observed if a random perturbation is introduced.

AB - We propose an analysis of the effects introduced by finite accuracy and round-off arithmetic on discrete dynamical systems. We investigate, from a statistical viewpoint and using the tool of the decay of fidelity, the error of the numerical orbit with respect to the exact one. As a model we consider a random perturbation of the exact orbit with an additive noise, for which exact results can be obtained for some prototype maps. For regular anysocrounous maps the fidelity has a power law decay, whereas the decay is exponential if a random perturbation is introduced. For chaotic maps the decay is superexponential after an initial plateau and our method is suitable to identify the reliability threshold of numerical results, i.e. a number of iterations below which global errors can be ignored. The same behaviour is observed if a random perturbation is introduced.

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U2 - 10.1209/0295-5075/89/40006

DO - 10.1209/0295-5075/89/40006

M3 - Article

AN - SCOPUS:79051471198

SN - 0295-5075

VL - 89

JO - Lettere Al Nuovo Cimento

JF - Lettere Al Nuovo Cimento

IS - 4

M1 - 40006

ER -