On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

We study the uniform approximation of the sigmoid cut function by smooth sigmoid functions such as the logistic and the Gompertz functions. The limiting case of the interval-valued В  step function is В  discussed В using В  Hausdorff metric. В Various expressions for the error estimates of the corr...

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Veröffentlicht in:Biomath (Sofia, Bulgaria) Bulgaria), 2015-10, Vol.4 (2)
Hauptverfasser: Iliev, Anton Iliev, Kyurkchiev, Nikolay, Markov, Svetoslav
Format: Artikel
Sprache:eng
Schlagworte:
cut function
Gompertz function
Hausdorff approximation
logistic function
sigmoid function
squashing function
step function
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Beschreibung
Zusammenfassung:We study the uniform approximation of the sigmoid cut function by smooth sigmoid functions such as the logistic and the Gompertz functions. The limiting case of the interval-valued В  step function is В  discussed В using В  Hausdorff metric. В Various expressions for the error estimates of the corresponding uniform and Hausdorff approximations are obtained. Numerical examples are presented using CAS MATHEMATICA.
ISSN:1314-684X
1314-7218
DOI:10.11145/j.biomath.2015.10.101