Approximation of Functions by Multivariable Hermite Basis: A Hybrid Method

  • Bartlomiej Beliczynski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6593)


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.


Function approximation Neural networks Orthonormal basis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bartlomiej Beliczynski
    • 1
  1. 1.Institute of Control and Industrial ElectronicsWarsaw University of TechnologyWarszawaPoland

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