Constructive Approximation

, Volume 5, Issue 1, pp 49–68 | Cite as

Symmetric iterative interpolation processes

  • Gilles Deslauriers
  • Serge Dubuc


Using a baseb and an even number of knots, we define a symmetric iterative interpolation process. The main properties of this process come from an associated functionF. The basic functional equation forF is thatF(t/b)=σnF(n/b)F(t-n). We prove thatF is a continuous positive definite function. We find almost precisely in which Lipschitz classes derivatives ofF belong. If a functiony is defined only on integers, this process extendsy continuously to the real axis asy(t=∑ n y(n)F(tn). Error bounds for this iterative interpolation are given.

AMS classification

65D05 41A05 65F15 15A18 42A38 26A16 65D10 42A05 65Q05 42A85 47B37 

Key words and phrases

Interpolation Eigenvalue Eigenvector Fourier transform Lipschitz classes Curve fitting Trigonometric polynomials Recurrence relations Factorization Operators in sequence spaces 


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  1. 1.
    S. Bochner, K. Chandrasekharan (1949): Fourier Transforms. Princeton: Princeton University Press.Google Scholar
  2. 2.
    G. Deslauriers, S. Dubuc (1987):Interpolation dyadique. In: Fractals. Dimensions non entières et applications. Paris: Masson, pp. 44–55.Google Scholar
  3. 3.
    G. Deslauriers, S. Dubuc (1987):Transformées de Fourier de courbes irrègulieres. Ann. Sci. Math. Québec,11:25–44.Google Scholar
  4. 4.
    S. Dubuc (1986):Interpolation through an iterative scheme. J. Math. Anal. Appl.,114:185–204.Google Scholar
  5. 5.
    A. O. Gel'fond (1971): Calculus of Finite Differences. Delhi: Hindustan.Google Scholar
  6. 6.
    B. B. Mandelbrot (1982): The Fractal Geometry of Nature. San Francisco: Freeman.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • Gilles Deslauriers
    • 1
  • Serge Dubuc
    • 2
  1. 1.Département de mathématiques appliquéesÉcole PolytechniqueMontréalCanada
  2. 2.Département de mathématiques et de statistiqueUniversité de MontréalMontréalCanada

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