Exact asymptotics of the optimal Lp-error of asymmetric linear spline approximation

• Vladislav Babenko ^[2] ; Yuliya Babenko ^[1] ; Nataliya Parfinovych ^[2] ; Dmytro Skorokhodov ^[2]
  1. [1] Kennesaw State University

     Kennesaw State University

     Estados Unidos

     
  2. [2] Dnepropetrovsk National University
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 6, Nº. 1, 2014, págs. 1-36
• Idioma: inglés
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• Resumen

  • In this paper we study the best asymmetric (sometimes also called penalized or sign-sensitive) approximation in the metrics of the space Lp, 1≤p ≥∞, of functions f ∈ C² (0, 1)² with nonnegative Hessian by piecewise linear splines s ∈ S(△N ), generated by given triangulations △N with N elements. We find the exact asymptotic behavior of the optimal (over triangulations △N and splines s ∈ S(△N )) error of such an approximation as N → ∞