On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

Kyurkchiev, Nikolay, and Markov, Svetoslav. "On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions." Serdica Journal of Computing 9.1 (2015): 93-104. <http://eudml.org/doc/281415>.

@article{Kyurkchiev2015,
abstract = {We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.},
author = {Kyurkchiev, Nikolay, Markov, Svetoslav},
journal = {Serdica Journal of Computing},
keywords = {Sigmoid Functions; Cut Function; Generalized Cut Function of Degree P+1; Step Function; Logistic Function; Shifted Logistic Function; Uniform and Hausdorff Approximation},
language = {eng},
number = {1},
pages = {93-104},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions},
url = {http://eudml.org/doc/281415},
volume = {9},
year = {2015},
}

TY - JOUR
AU - Kyurkchiev, Nikolay
AU - Markov, Svetoslav
TI - On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions
JO - Serdica Journal of Computing
PY - 2015
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 9
IS - 1
SP - 93
EP - 104
AB - We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.
LA - eng
KW - Sigmoid Functions; Cut Function; Generalized Cut Function of Degree P+1; Step Function; Logistic Function; Shifted Logistic Function; Uniform and Hausdorff Approximation
UR - http://eudml.org/doc/281415
ER -