The shape parameter in the Gaussian function

DOI10.1016/j.camwa.2011.11.032zbMath1238.41014arXiv1006.2318OpenAlexW2004312146MaRDI QIDQ418384

J. Herrera, H. S. Yoon

Publication date: 28 May 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.2318

zbMATH Keywords

interpolationGaussianradial basis functionshape parameter

Mathematics Subject Classification ID

Numerical interpolation (65D05) Multidimensional problems (41A63) Approximation by other special function classes (41A30)

Related Items (12)

On flexibility of constraints system under approximation of optimal control problems ⋮ A numerical study of Asian option with radial basis functions based finite differences method ⋮ On monotone approximation of piecewise continuous monotone functions with the help of translations and dilations of the Laplace integral ⋮ Gaussian functions combined with Kolmogorov's theorem as applied to approximation of functions of several variables ⋮ A comparison of the meshless RBF collocation method with finite element and boundary element methods in neutron diffusion calculations ⋮ Optimization, conditioning and accuracy of radial basis function method for partial differential equations with nonlocal boundary conditions -- a case of two-dimensional Poisson equation ⋮ The shape parameter in the Gaussian function. II ⋮ On the search of the shape parameter in radial basis functions using univariate global optimization methods ⋮ On the new variable shape parameter strategies for radial basis functions ⋮ On the application of Gaussian functions for discretization of optimal control problems ⋮ Local variably scaled Newton basis functions collocation method for solving Burgers' equation ⋮ An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing

Cites Work

• Multiscale analysis in Sobolev spaces on bounded domains
• Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions
• The mystery of the shape parameter. III
• Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
• Miscellaneous error bounds for multiquadric and related interpolators
• The mystery of the shape parameter. IV
• The crucial constants in the exponential-type error estimates for Gaussian interpolation
• Local error estimates for radial basis function interpolation of scattered data
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• Scattered Data Approximation
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