A note on tensor product spline approximation via extension operators

• Bernhard Mößner ^[1] ; Nada Sissouno ^[2]
  1. [1] Reutlingen University

     Reutlingen University

     Distrito de Reutlingen, Alemania

     
  2. [2] University of Passau

     University of Passau

     Kreisfreie Stadt Passau, Alemania

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 8, Nº. 1, 2016, págs. 27-32
• Idioma: inglés
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• Resumen

  • 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.