Sobolev-type approximation rates for divergence-free and curl-free RBF interpolants

DOI10.1090/S0025-5718-07-02096-0zbMath1196.41003OpenAlexW2021218667MaRDI QIDQ3577005

Edward J. Fuselier

Publication date: 3 August 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-02096-0

zbMATH Keywords

error estimatesinterpolation of multivariate functionradial basis function interpolant

Mathematics Subject Classification ID

Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Approximation by other special function classes (41A30)

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Cites Work

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• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions
• Recent developments in error estimates for scattered-data interpolation via radial basis functions
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Error estimates for matrix-valued radial basis function interpolation
• Norms of inverses and condition numbers for matrices associated with scattered data
• Finite Element Methods for Navier-Stokes Equations
• Generalized Hermite Interpolation Via Matrix-Valued Conditionally Positive Definite Functions
• Scattered-Data Interpolation on $\bb R^\protectn$: Error Estimates for Radial Basis and Band-Limited Functions
• Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
• Scattered Data Interpolation on Spheres: Error Estimates and Locally Supported Basis Functions
• Approximation orders for interpolation by surface splines to rough functions
• Scattered Data Approximation