Smoothness and error bounds of Martensen splines

• Vittoria Demichelis ^[1] ; Matteo Sciarra ^[1]
  1. [1] University of Torino
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 278, Nº 1 (15 April 2015), 2015, págs. 90-100
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.09.027
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• Resumen

  • Martensen splines MfMf of degree nn interpolate ff and its derivatives up to the order n−1n−1 at a subset of the knots of the spline space, have local support and exactly reproduce both polynomials and splines of degree ≤n≤n. An approximation error estimate has been provided for f∈Cn+1f∈Cn+1.

    This paper aims to clarify how well the Martensen splines MfMf approximate smooth functions on compact intervals. Assuming that f∈Cn−1f∈Cn−1, approximation error estimates are provided for Djf,j=0,1,…,n−1Djf,j=0,1,…,n−1, where DjDj is the jth derivative operator. Moreover, a set of sufficient conditions on the sequence of meshes are derived for the uniform convergence of DjMfDjMf to DjfDjf, for j=0,1,…,n−1j=0,1,…,n−1.