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

Kyurkchiev, Nikolay; Markov, Svetoslav

Serdica Journal of Computing (2015)

- Volume: 9, Issue: 1, page 93-104
- ISSN: 1312-6555

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topKyurkchiev, 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 -

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