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L p error estimates for approximation by Sobolev splines and Wendland functions on ℝd

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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.

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Authors and Affiliations

  1. Biomedical Imaging Group, EPFL, 1015, Lausanne, Switzerland

    John Paul Ward

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  1. John Paul Ward
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Correspondence to John Paul Ward.

Additional information

Communicated by R. Schaback.

This paper contains work from the author’s dissertation written under the supervision of Professors F. J. Narcowich and J. D. Ward at Texas A&M University. This research was supported by grant DMS-0807033 from the National Science Foundation.

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Ward, J.P. L p error estimates for approximation by Sobolev splines and Wendland functions on ℝd . Adv Comput Math 38, 873–889 (2013). https://doi.org/10.1007/s10444-011-9263-7

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  • DOI: https://doi.org/10.1007/s10444-011-9263-7

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