Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2009; 46(4): 701-712

Printed July 1, 2009

https://doi.org/10.4134/BKMS.2009.46.4.701

Copyright © The Korean Mathematical Society.

The simultaneous approximation order by neural networks with a squashing function

Nahmwoo Hahm

University of Incheon

Abstract

In this paper, we study the simultaneous approximation to functions in $C^m [0,1]$ by neural networks with a squashing function and the complexity related to the simultaneous approximation using a Bernstein polynomial and the modulus of continuity. Our proofs are constructive.

Keywords: simultaneous approximation, Bernstein polynomial, squashing function, neural network

MSC numbers: Primary 41A10, 41A29, 65D15

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