# Modiﬁed Kolmogorov’s theorem

Mathematica Applicanda (2009)

- Volume: 37, Issue: 51/10
- ISSN: 1730-2668

## Access Full Article

top## Abstract

top## How to cite

topJarosław 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.