Modified Kolmogorov’s theorem

Jarosław Michalkiewicz. "Modified Kolmogorov’s theorem." Mathematica Applicanda 37.51/10 (2009): null. <http://eudml.org/doc/292805>.

@article{JarosławMichalkiewicz2009,
abstract = {The article takes up the modification of the Kolmogorov’s representation theorem of a multivariant continuous function as a superposition of one continuous function, called internal, with many continuous functions, called external, all of one variable. The Kolmogorov’s theorem does not determine how to find the internal function.Author suggests an application of functions of particular forms.This requires a modification of the theorem.The form of the Kolmogorov’s theorem modified by the Author finds its application in the theory and practise of neural networks and in the identification of objects in the automatics.The modified Kolmogorov’s theorem enables the author to construct a simple computer algorithm.},
author = {Jarosław Michalkiewicz},
journal = {Mathematica Applicanda},
keywords = {approximation, Kolmogorov’s theorem, non-linear dynamical systems},
language = {eng},
number = {51/10},
pages = {null},
title = {Modified Kolmogorov’s theorem},
url = {http://eudml.org/doc/292805},
volume = {37},
year = {2009},
}

TY - JOUR
AU - Jarosław Michalkiewicz
TI - Modified Kolmogorov’s theorem
JO - Mathematica Applicanda
PY - 2009
VL - 37
IS - 51/10
SP - null
AB - The article takes up the modification of the Kolmogorov’s representation theorem of a multivariant continuous function as a superposition of one continuous function, called internal, with many continuous functions, called external, all of one variable. The Kolmogorov’s theorem does not determine how to find the internal function.Author suggests an application of functions of particular forms.This requires a modification of the theorem.The form of the Kolmogorov’s theorem modified by the Author finds its application in the theory and practise of neural networks and in the identification of objects in the automatics.The modified Kolmogorov’s theorem enables the author to construct a simple computer algorithm.
LA - eng
KW - approximation, Kolmogorov’s theorem, non-linear dynamical systems
UR - http://eudml.org/doc/292805
ER -