A new class of radial basis functions with compact support
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This paper studies a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier in the literature.Abstract:
Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier in the literature.read more
Citations
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References
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Book
Introduction to Fourier Analysis on Euclidean Spaces.
Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
Journal ArticleDOI
Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
TL;DR: A new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support is constructed, it is proved that they are of minimal degree and unique up to a constant factor.
Book ChapterDOI
Interpolation of scattered data: Distance matrices and conditionally positive definite functions
TL;DR: In this paper, it was shown that multiquadric surface interpolation is always solvable, thereby settling a conjecture of R Franke, which is a conjecture that was later proved in the present paper.
Journal ArticleDOI
Local error estimates for radial basis function interpolation of scattered data
Zongmin Wu,Robert Schaback +1 more
TL;DR: In this article, a suitable variational formulation for the local error of scattered data intepolation by radial basis functions φ(r) was proposed, where the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain Kriging function.