Closed form representations for a class of compactly supported radial basis functions

DOI10.1007/s10444-011-9184-5zbMath1251.41007OpenAlexW2158801567MaRDI QIDQ429791

Simon Hubbert

Publication date: 20 June 2012

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-011-9184-5

zbMATH Keywords

hypergeometric functionspositive definite functionsassociated Legendre functionscompactly supported radial basis functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Positive definite functions in one variable harmonic analysis (42A82) Interpolation in approximation theory (41A05) Spline approximation (41A15) Classical hypergeometric functions, ({}_2F_1) (33C05) Approximation by other special function classes (41A30)

Related Items (11)

Summation of Gaussian shifts as Jacobi's third theta function ⋮ Compactly-supported isotropic covariances on spheres obtained from matrix-valued covariances in Euclidean spaces ⋮ Constructing radial kernels with higher-order generalized Strang-Fix conditions ⋮ Wendland functions with increasing smoothness converge to a Gaussian ⋮ TV-based reconstruction of periodic functions ⋮ Closed form representations and properties of the generalised Wendland functions ⋮ Unifying compactly supported and Matérn covariance functions in spatial statistics ⋮ Convergence of the Smoothed Particle Hydrodynamics Method for a Specific Barotropic Fluid Flow: Constructive Kernel Theory ⋮ Estimation and prediction of Gaussian processes using generalized Cauchy covariance model under fixed domain asymptotics ⋮ Unnamed Item ⋮ An Improved Convergence Result for the Smoothed Particle Hydrodynamics Method

Cites Work

• Unnamed Item
• The missing Wendland functions
• On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
• Operators on radial functions
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Grünbaum's inequality for Bessel functions
• Scattered Data Approximation

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