Kernel based approximation in Sobolev spaces with radial basis functions

DOI10.1016/j.amc.2009.08.012zbMath1179.65016OpenAlexW1973296370MaRDI QIDQ1039692

Limin Ma, Zong Min Wu

Publication date: 23 November 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.08.012

zbMATH Keywords

error estimatesradial basis functionreproducing kernel Hilbert spacescattered data approximationminimal norm interpolationsmoothing by convolution

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items

Unconditionally stable meshless integration of time-domain Maxwell's curl equations ⋮ Surrogate modeling of multiscale models using kernel methods ⋮ Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems ⋮ Imposing various boundary conditions on positive definite kernels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A unified theory of radial basis functions. Native Hilbert spaces for radial basis functions. II
• Approximation in Sobolev spaces by kernel expansions
• Compactly supported positive definite radial functions
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Approximation by radial basis functions with finitely many centers
• Local error estimates for radial basis function interpolation of scattered data
• Meshless Galerkin methods using radial basis functions
• Radial Basis Functions
• Scattered Data Approximation
• Approximation in \(L_p (\mathbb{R}^d)\) from a space spanned by the scattered shifts of a radial basis function