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A note on tensor product spline approximation via extension operators

  • In this note we look at anisotropic approximation of smooth functions on bounded domains with tensor product splines. The main idea is to extend such functions and then use known approximation techniques on Rd. We prove an error estimate for domains for which bounded extension operators exist. This obvious approach has some limitations. It is not applicable without restrictions on the chosen coordinate degree even if the domain is as simple as the unit disk. Further for approximation on Rd there are error estimates in which the grid widths and directional derivatives are paired in an interesting way. It seems impossible to maintain this property using extension operators.

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Author of HS ReutlingenMößner, Bernhard
Erschienen in:Jaén journal on approximation : revista matemática internacional
Publisher:Univ. de Jaén
Place of publication:Jaén
Document Type:Journal article
Publication year:2016
Tag:anisotropic; approximation; extensions; splines
Page Number:6
First Page:27
Last Page:32
DDC classes:510 Mathematik
Open access?:Nein