Hermite interpolation using ERBS with trigonometric polynomial local functions

  • Authors:

  • Lubomir T. Dechevsky;Rumen Uluchev

  • Affiliations:

  • Narvik University College, Narvik, Norway;University of Transport (VTU), Sofia, Bulgaria

  • Venue:
  • LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
  • Year:
  • 2011

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Abstract

Given a sequence of knots t0 t1 tn+1 , an expo-rational B-spline (ERBS) function f(t) is defined by $$ f(t)=\sum_{k=1}^n \ell_k(t)B_k(t), \quad t\in[t_1,t_n], $$ where Bk (t) are the ERBS and ℓk (t) are local functions defined on (tk−1 ,tk+1 ). Consider the Hermite interpolation problem at the knots 0≤t1 t2 tn π of arbitrary multiplicities. In [3] a formula was suggested for Hermite-interpolating ERBS function with ℓk (t) being algebraic polynomials. Here we construct Hermite interpolation by an ERBS function with trigonometric polynomial local functions. We provide also numerical results for the performance of the new trigonometric ERBS (TERBS) interpolant in graphical comparison with the interpolant from [3]. Potential applications and some topics for further research on TERBS are briefly outlined.