A method of multivariable Hermite basis function approximation

作者：Beliczynski Bartlomiej^*

来源：Neurocomputing, 2012, 96: 12-18.

DOI：10.1016/j.neucom.2011.10.035

• Function approximation
• Orthonormal basis
• Hermite functions

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.

• 出版日期2012-11-1