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\iteman{io-port 06075802}
\itemau{Beliczynski, Bartlomiej}
\itemti{A method of multivariable Hermite basis function approximation.}
\itemso{Neurocomputing 96, 12-18 (2012).}
\itemab
Summary: A method of multivariable (multivariate) Hermite function based approximation is presented and discussed. The multivariable basis is constructed as a product of one-variable Hermite functions with adjustable scaling parameters. Thanks basis orthonormality, the approximated function expansion coefficients are calculated by using explicit, non-search formulae. The scaling parameters are determined via a search algorithm. Initially, an excessive number of functions in the basis is calculated, then a simple pruning method is applied. Only those are taken which contribute the most to error decrease, down to a desired level. The method ensures a very good generalization property. This claim is supported by both theoretical considerations and working examples.
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\itemcc{}
\itemut{function approximation; orthonormal basis; Hermite functions}
\itemli{doi:10.1016/j.neucom.2011.10.035}
\end