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

Anton Iliev Iliev, Nikolay Kyurkchiev, Svetoslav Markov

Abstract


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   step function is   discussed  using   Hausdorff metric.  Various expressions for the error estimates of the corresponding uniform and Hausdorff approximations are obtained. Numerical examples are presented using CAS MATHEMATICA.

Keywords


cut function; step function; sigmoid function; logistic function; Gompertz function; squashing function; Hausdorff approximation.

Full Text:

PDF


DOI: http://dx.doi.org/10.11145/j.biomath.2015.10.101

Refbacks

  • There are currently no refbacks.


ISSN 1314-7218 (online)
ISSN 1314-684X (print)

Indexed by: Mathematical Reviews (MathSciNet), Zentralblatt MATH, Academic Serach Premier, Academic Search Elite, Academic Search Complete, Academic Search Ultimate