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. © 2011 Springer-Verlag.
CITATION STYLE
Beliczynski, B. (2011). Approximation of functions by multivariable hermite basis: A hybrid method. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6593 LNCS, pp. 130–139). https://doi.org/10.1007/978-3-642-20282-7_14
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