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Recursive polynomial interpolation algorithm (RPIA)

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Abstract

Let x 0, x 1, ⋯ , x n be a set of n+1 distinct real numbers (i.e., x i ≠ x j for i ≠ j) and y 0, y 1, ⋯ , y n be given real numbers; we know that there exists a unique polynomial p n (x) of degree n such that p n (x i ) = y i for i = 0, 1, ⋯ , n; p n is the interpolation polynomial for the set {(x i , y i ), i = 0, 1, ⋯ , n}. The polynomial p n (x) can be computed by using the Lagrange method or the Newton method. This paper presents a new method for computing interpolation polynomials. We will reformulate the interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the recursive polynomial interpolation algorithm (RPIA). Some properties of this algorithm will be studied and some examples will also be given.

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Authors and Affiliations

  1. Ecole Normale Supérieure, Mohammed V University in Rabat, Av. Mohammed Belhassan El Ouazzan, B.P. 5118, Takaddoum, Rabat, Morocco

    Abderrahim Messaoudi

  2. L.M.P.A, Université du Littoral Côte d’Opale, 50 rue F. Buisson BP 699, 62228, Calais Cedex, France

    Hassane Sadok

Authors
  1. Abderrahim Messaoudi
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  2. Hassane Sadok
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Correspondence to Hassane Sadok.

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Messaoudi, A., Sadok, H. Recursive polynomial interpolation algorithm (RPIA). Numer Algor 76, 675–694 (2017). https://doi.org/10.1007/s11075-017-0276-2

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  • DOI: https://doi.org/10.1007/s11075-017-0276-2

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