Inverse and saturation theorems for radial basis function interpolation

DOI10.1090/S0025-5718-01-01383-7zbMath0989.41002MaRDI QIDQ2781215

Robert Schaback, Holger Wendland

Publication date: 19 March 2002

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

zbMATH Keywords

interpolationpositive definite functionsapproximation orders

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Interpolation in approximation theory (41A05) Approximation by other special function classes (41A30) Inverse theorems in approximation theory (41A27) Saturation in approximation theory (41A40)

Related Items

Approximation of eigenfunctions in kernel-based spaces, A level set method for topological shape optimization of 3D structures with extrusion constraints, Design of distributed compliant micromechanisms with an implicit free boundary representation, Summation of Gaussian shifts as Jacobi's third theta function, \(L^2\) error estimates of unsymmetric RBF collocation for second order quasilinear elliptic equations, Spherical basis functions and uniform distribution of points on spheres, A nonlinear discretization theory for meshfree collocation methods applied to quasilinear elliptic equations, Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis, An inverse theorem for compact Lipschitz regions in ℝ^{𝕕} using localized kernel bases, Shape and topology optimization of compliant mechanisms using a parameterization level set method, A short note on the comparison of interpolation widths, entropy numbers, and Kolmogorov widths, Regularized kernel-based reconstruction in generalized Besov spaces, \(L^p\) Bernstein inequalities and inverse theorems for RBF approximation on \(\mathbb{R}^d\), A study of the uniform accuracy of univariate thin plate spline interpolation, Recovery of functions from weak data using unsymmetric meshless kernel-based methods, $L^p$ Bernstein estimates and approximation by spherical basis functions, On the semi-norm of radial basis function interpolants, Sampling and Stability, Power series kernels, A level set-based parameterization method for structural shape and topology optimization

Cites Work

• Error estimates for interpolation by compactly supported radial basis functions of minimal degree
• Local accuracy for radial basis function interpolation on finite uniform grids
• On power functions and error estimates for radial basis function interpolation
• A unified theory of radial basis functions. Native Hilbert spaces for radial basis functions. II
• Error estimates and condition numbers for radial basis function interpolation
• Local error estimates for radial basis function interpolation of scattered data
• Sur l’erreur d’interpolation des fonctions de plusieurs variables par les $D^m$-splines
• Improved error bounds for scattered data interpolation by radial basis functions
• Error estimates for scattered data interpolation on spheres
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• Interpolation by polynomials and radial basis functions on spheres
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item