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

By Anton I. Iliev, Nikolay Kyurkchiev, Svetoslav M. Markov. 2015

57 citations recorded by the source corpus.

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.

Subfields: Information Systems, Mechanical Engineering, Nature and Landscape Conservation

View Paper: https://www.semanticscholar.org/paper/72a576a56814bbdfdf77680974df80ca989d4290

Citations in the corpus

• On the Hausdorff distance between the Heaviside step function and Verhulst logistic function (2015, unknown): “About approximation of the cut function by logistic and squashing functions see, [7,8,13,15,18].”