$C^\infty$ Compactly Supported and Positive Definite Radial Kernels

Numerical interpolation (65D05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Algorithms for approximation of functions (65D15)

Uses Software

Matlab
Chebfun
rbf_qr

Cites Work

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The orthogonal gradients method: a radial basis functions method for solving partial differential equations on arbitrary surfaces
A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere
Wendland functions with increasing smoothness converge to a Gaussian
The missing Wendland functions
Stabilization of RBF-generated finite difference methods for convective PDEs
Eigenvalue stability of radial basis function discretizations for time-dependent problems
Error saturation in Gaussian radial basis functions on a finite interval
Interpolation in the limit of increasingly flat radial basis functions
Computing eigenmodes of elliptic operators using radial basis functions
Stable computation of multiquadric interpolants for all values of the shape parameter
Compactly supported correlation functions
Overlapping domain decomposition method by radial basis functions
Compactly supported positive definite radial functions
Natural convection in rectangular enclosures heated from one side and cooled from the ceiling
Multivariate interpolation by polynomials and radial basis functions
The Runge phenomenon and spatially variable shape parameters in RBF interpolation
Limit problems for interpolation by analytic radial basis functions
Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions
Natural convection in rectangular tanks heated locally from below
Stable Computation of Differentiation Matrices and Scattered Node Stencils Based on Gaussian Radial Basis Functions
An Algorithm for the Convolution of Legendre Series
Stable Evaluation of Gaussian Radial Basis Function Interpolants
Piecewise-smooth chebfuns
Stable Computations with Gaussian Radial Basis Functions
How fast do radial basis function interpolants of analytic functions converge?
Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
A Stable Algorithm for Flat Radial Basis Functions on a Sphere
An Algorithm for Finding Best Matches in Logarithmic Expected Time
Generalized Hermite Interpolation Via Matrix-Valued Conditionally Positive Definite Functions
NUMERICAL SIMULATION OF TWO-DIMENSIONAL BUOYANCY-DRIVEN TURBULENCE IN A TALL RECTANGULAR CAVITY
Radial Basis Functions
Spectral Methods in MATLAB
Barycentric Lagrange Interpolation
A Practical Guide to Pseudospectral Methods
Convergence of Increasingly Flat Radial Basis Interpolants to Polynomial Interpolants
Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation
Scattered Data Approximation

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