Best approximation properties and error bounds of gaussian networks

Binfan Liu; Jennie Si

Best approximation properties and error bounds of gaussian networks

Binfan Liu, Jennie Si

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Scopus citations

Abstract

The best approximation of any C² function with support on the unit hypercube I_m in R^m is considered in the present paper. We prove that a Gaussian radial basis network with centers defined on a regular mesh in R^m has the best approximation property. Moreover, an upper bound (O(N^MIN2)) of the approximation is obtained for a network having N^m units.

Original language	English (US)
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Editors	Anon
Publisher	Publ by IEEE
Pages	2798-2801
Number of pages	4
ISBN (Print)	0780312988
State	Published - Dec 1 1993
Event	Proceedings of the 32nd IEEE Conference on Decision and Control. Part 3 (of 4) - San Antonio, TX, USA Duration: Dec 15 1993 → Dec 17 1993

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	3
ISSN (Print)	0191-2216

Other

Other	Proceedings of the 32nd IEEE Conference on Decision and Control. Part 3 (of 4)
City	San Antonio, TX, USA
Period	12/15/93 → 12/17/93

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Cite this

Liu, B & Si, J 1993, Best approximation properties and error bounds of gaussian networks. in Anon (ed.), Proceedings of the IEEE Conference on Decision and Control. Proceedings of the IEEE Conference on Decision and Control, vol. 3, Publ by IEEE, pp. 2798-2801, Proceedings of the 32nd IEEE Conference on Decision and Control. Part 3 (of 4), San Antonio, TX, USA, 12/15/93.

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AB - The best approximation of any C2 function with support on the unit hypercube Im in Rm is considered in the present paper. We prove that a Gaussian radial basis network with centers defined on a regular mesh in Rm has the best approximation property. Moreover, an upper bound (O(NMIN2)) of the approximation is obtained for a network having Nm units.

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M3 - Conference contribution

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BT - Proceedings of the IEEE Conference on Decision and Control

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ER -

Best approximation properties and error bounds of gaussian networks

Abstract

Publication series

Other

ASJC Scopus subject areas

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