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On the relations between finite differences and derivatives of cardinal spline functions

  • Hennie ter Morsche
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 501)

Abstract

Let m be a natural number and let Sm denote the class of cardinal spline functions of degree m. The object of this note is to establish a linear relationship between the 2m+2 quantities s(i+x), s(i+1+x),...,s(i+m+x), s(k)(i+y), s(k)(i+1+y),...,s(k)(i+m+y), where x,y ∈ [0,1], i=0,±1,±2,... s ∈ Sm and where s(k) denotes the k-th derivative of s (k=0,1,2,...,m−1). Using the shift operator E, we represent this relation in a simple form, involving the exponential Euler polynomials. The results are applied to cardinal spline interpolation.

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References

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Hennie ter Morsche
    • 1
  1. 1.Department of MathematicsTechnological University EindhovenEindhovenThe Netherlands

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