Numerical integration on multivariate scattered data by Lobachevsky splines

  • Authors:

  • Giampietro Allasia;Roberto Cavoretto;Alessandra De Rossi

  • Affiliations:

  • Department of Mathematics ‘G. Peano’, University of Turin, Via Carlo Alberto 10, I – 10123, Turin, Italy;Department of Mathematics ‘G. Peano’, University of Turin, Via Carlo Alberto 10, I – 10123, Turin, Italy;Department of Mathematics ‘G. Peano’, University of Turin, Via Carlo Alberto 10, I – 10123, Turin, Italy

  • Venue:
  • International Journal of Computer Mathematics
  • Year:
  • 2013

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Abstract

In this paper, we investigate the numerical integration problem of a real valued function generally known only on multivariate scattered points using Lobachevsky splines, a pioneering version of cardinal B-splines. Starting from their interpolation properties, we focus on the construction of new integration formulas, which are quite flexible requiring no special distribution of nodes. Numerical results using Lobachevsky splines turn out to be interesting and promising for both accuracy and simplicity in computation. Finally, a comparison with integration by radial basis functions confirms the validity of the proposed approach.