Embeddings of Beppo–Levi spaces in Hölder–Zygmund spaces, and a new method for radial basis function interpolation error estimates

The Beppo–Levi native spaces which arise when using polyharmonic splines to interpolate in many space dimensions are embedded in Hölder–Zygmund spaces. Convergence rates for radial basis function interpolation are inferred in some special cases.

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Bibliographic Details
Published inJournal of approximation theory Vol. 137; no. 2; pp. 166 - 178
Main Authors Beatson, R.K., Bui, H.-Q., Levesley, J.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2005
Subjects
Beppo–Levi spaces
Embedding theorem
Error estimates
Polyharmonic splines
Radial basis functions
Beppo–Levi spaces
Radial basis functions
Error estimates
41A25
46E35
Polyharmonic splines
Embedding theorem
41A05
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Summary:The Beppo–Levi native spaces which arise when using polyharmonic splines to interpolate in many space dimensions are embedded in Hölder–Zygmund spaces. Convergence rates for radial basis function interpolation are inferred in some special cases.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2005.07.009