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

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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.
Original languageEnglish
Title of host publicationSpline Functions (Proceedings International Symposium, Karlsruhe, Germany, 1975)
EditorsK. Boehmer, G. Meinardus, W. Schempp
Place of PublicationBerlin
PublisherSpringer
Pages210-219
Number of pages10
ISBN (Electronic)978-3-540-38073-3
ISBN (Print)978-3-540-07543-1
DOIs
Publication statusPublished - 1976

Publication series

NameLecture Notes in Mathematics
Volume501
ISSN (Print)0075-8434

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  • Cite this

    Morsche, ter, H. G. (1976). On the relations between finite differences and derivatives of cardinal spline functions. In K. Boehmer, G. Meinardus, & W. Schempp (Eds.), Spline Functions (Proceedings International Symposium, Karlsruhe, Germany, 1975) (pp. 210-219). (Lecture Notes in Mathematics; Vol. 501). Berlin: Springer. https://doi.org/10.1007/BFb0079749