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.
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Beliczynski, B. (2011). Approximation of Functions by Multivariable Hermite Basis: A Hybrid Method. In: Dobnikar, A., Lotrič, U., Šter, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2011. Lecture Notes in Computer Science, vol 6593. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20282-7_14
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DOI: https://doi.org/10.1007/978-3-642-20282-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20281-0
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