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Mathematics > Classical Analysis and ODEs

arXiv:1103.5997 (math)
[Submitted on 30 Mar 2011 (v1), last revised 27 Feb 2012 (this version, v2)]

Title:$L^p$ Error Estimates for Approximation by Sobolev Splines and Wendland Functions on $\mathbb{R}^d$

Authors:John Paul Ward
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Abstract:It is known that a Green's function-type condition may be used to derive rates for approximation by radial basis functions (RBFs). In this paper, we introduce a method for obtaining rates for approximation by functions which can be convolved with a finite Borel measure to form a Green's function. Following a description of the method, rates will be found for two classes of RBFs. Specifically, rates will be found for the Sobolev splines, which are Green's functions, and the perturbation technique will then be employed to determine rates for approximation by Wendland functions.
Subjects: Classical Analysis and ODEs (math.CA)
Cite as: arXiv:1103.5997 [math.CA]
  (or arXiv:1103.5997v2 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.1103.5997
Journal reference: Adv. Comput. Math., May 2013, Volume 38, Issue 4, pp 873-889
Related DOI: https://doi.org/10.1007/s10444-011-9263-7

Submission history

From: John Ward [view email]
[v1] Wed, 30 Mar 2011 17:25:42 UTC (13 KB)
[v2] Mon, 27 Feb 2012 16:35:09 UTC (15 KB)
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