On a generalized Gaussian radial basis function: Analysis and applications

By Nader Karimi, Saeed Kazem, D. Ahmadian, Hojatollah Adibi, L. Ballestra. 2020

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Abstract We introduce a new infinitely smooth generalized Gaussian radial basis function (GGRBF) involving two shape parameters: ψ ( r ; ϵ ; ϵ 0 ) = φ ( r ; ϵ ) exp ( φ ( r ; ϵ 0 ) − 1 ) , where φ(r; ϵ) is the Gaussian basis associated with the shape parameter ϵ and ϵ0 is an auxiliary shape parameter. A thorough theoretical analysis is performed proving that the proposed radial basis function is strictly positive definite and, when it is used for function approximation, yields exponential convergence rate. In addition, we show, both analytically and numerically, that, by suitably choosing the second auxiliary parameter, the ill-conditioning problems that usually occur because of flat radial basis can be avoided. The reported numerical experiments highlight the very satisfactory performances of the novel radial basis function.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a673a06aefd45cc3d6e849abb86b57f6681e58f9