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Refined Error Estimates for Radial Basis Function Interpolation

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Constructive Approximation Aims and scope

We discuss new and refined error estimates for radial-function scattered-data interpolants and their derivatives. These estimates hold on R d, the d-torus, and the 2-sphere. We employ a new technique, involving norming sets, that enables us to obtain error estimates, which in many cases give bounds orders of magnitude smaller than those previously known.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M; University, College Station, TX 77843-3368, USA

    F.J. Narcowich & J.D. Ward

  2. Universität Göttingen, Lotzestrasse 16-18, D-37083, Göttingen, Germany

    H. Wendland

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  1. F.J. Narcowich
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  2. J.D. Ward
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  3. H. Wendland
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Correspondence to H. Wendland.

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Communicated by Ronald A. DeVore

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Narcowich, F., Ward, J. & Wendland, H. Refined Error Estimates for Radial Basis Function Interpolation. Constr. Approx. 19, 541–564 (2003). https://doi.org/10.1007/s00365-002-0529-7

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  • DOI: https://doi.org/10.1007/s00365-002-0529-7

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