Interpolation by radial functions on Sobolev space

DOI10.1006/jath.2001.3584zbMath0992.41005OpenAlexW2036164825MaRDI QIDQ5958883

Jungho Yoon

Publication date: 10 September 2002

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.2001.3584

zbMATH Keywords

interpolationSobolev spaceradial basis functionsGaussianmultiquadricsshifted surface splines

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05)

Related Items (8)

Quick approximation of bivariate functions ⋮ $L_p$-error estimates for ``shifted surface spline interpolation on Sobolev space ⋮ Shape variable radial basis function and its application in dual reciprocity boundary face method ⋮ Improved accuracy of \(L_{p}\)-approximation to derivatives by radial basis function interpolation ⋮ Function approximation on non-Euclidean spaces ⋮ Error estimates for interpolation of rough data using the scattered shifts of a radial basis function ⋮ Approximation using scattered shifts of a multivariate function ⋮ Radial basis collocation methods for elliptic boundary value problems

Cites Work

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• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
• Fourier analysis of the approximation power of principal shift-invariant spaces
• Regarding the \(p\)-norms of radial basis interpolation matrices
• Error estimates and condition numbers for radial basis function interpolation
• Approximation by radial basis functions with finitely many centers
• Local error estimates for radial basis function interpolation of scattered data
• The approximation power of moving least-squares
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• Approximation in \(L_p (\mathbb{R}^d)\) from a space spanned by the scattered shifts of a radial basis function
• Computational aspects of approximation to scattered data by using `shifted' thin-plate splines

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