Approximation in \(L_p (\mathbb{R}^d)\) from a space spanned by the scattered shifts of a radial basis function

DOI10.1007/s003650010033zbMath0994.41019OpenAlexW2129382345MaRDI QIDQ5937039

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Publication date: 8 October 2002

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s003650010033

zbMATH Keywords

radial basis functionapproximation of scattered dataapproximation of Sobolev space functionsapproximation orderlocal approximation schememultiquadricssmoothing effectsurface spline

Mathematics Subject Classification ID

Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15) Approximation by other special function classes (41A30)

Related Items

$L_p$-error estimates for ``shifted surface spline interpolation on Sobolev space ⋮ On the stationary \(L_{p}\)-approximation power to derivatives by radial basis function interpolation. ⋮ Optimality and Regularization Properties of Quasi-Interpolation: Deterministic and Stochastic Approaches ⋮ Multivariate Monte Carlo Approximation Based on Scattered Data ⋮ Generalized Strang-Fix condition for scattered data quasi-interpolation ⋮ Interpolation by radial functions on Sobolev space ⋮ Approximation using scattered shifts of a multivariate function ⋮ A non-stationary approximation scheme on scattered centers in \({\mathbb R}^{d}\) by radial basis functions. ⋮ Kernel based approximation in Sobolev spaces with radial basis functions ⋮ Multivariate quasi-interpolation inL^p(ℝ^d) with radial basis functions for scattered data ⋮ Sampling inequalities for infinitely smooth radial basis functions and its application to error estimates

Cites Work

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