Approximation of functions by multivariable hermite basis: a hybrid method

Authors:
Bartlomiej Beliczynski
Affiliations:
Warsaw University of Technology, Institute of Control and Industrial Electronics, Warszawa, Poland
Venue:
ICANNGA'11 Proceedings of the 10th international conference on Adaptive and natural computing algorithms - Volume Part I
Year:
2011

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Abstract

In this paper an approximation of multivariable functions by Hermite basis is presented and discussed. Considered here basis is constructed as a product of one-variable Hermite functions with adjustable scaling parameters. The approximation is calculated via hybrid method, the expansion coefficients by using an explicit, non-search formulae, and scaling parameters are determined via a search algorithm. A set of excessive number of Hermite functions is initially calculated. To constitute the approximation basis only those functions are taken which ensure the fastest error decrease down to a desired level. Working examples are presented, demonstrating a very good generalization property of this method.