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A Family of Spline Quasi-Interpolants on the Sphere

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Abstract

In this paper, we construct a local quasi-interpolant Q for fitting a function f defined on the sphere S. We first map the surface S onto a rectangular domain and next, by using the tensor product of polynomial splines and 2π-periodic trigonometric splines, we give the expression of Qf. The use of trigonometric splines is necessary to enforce some boundary conditions which are useful to ensure the C 2 continuity of the associated surface. Finally, we prove that Q realizes an accuracy of optimal order.

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Authors and Affiliations

  1. Département de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed I, Oujda, Maroc

    O. Nouisser & D. Sbibih

  2. INSA, 20 avenue des Buttes de Coesmes, CS 14315, 35043, Rennes Cédex, France

    Paul Sablonnière

Authors
  1. O. Nouisser
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  2. D. Sbibih
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  3. Paul Sablonnière
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Nouisser, O., Sbibih, D. & Sablonnière, P. A Family of Spline Quasi-Interpolants on the Sphere. Numerical Algorithms 33, 399–413 (2003). https://doi.org/10.1023/A:1025549029512

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