Polynomial Splines and Difference Equations

  • Günter Meinardus
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)


This is an elementary introduction to polynomial spline functions. The existence and uniqueness of the B-splines is proved. A special representation of those functions leads to many properties and, in particular, to the fact that they form a basis of the splines. The concept of linear difference equation is discussed. Eventually the connection of spline interpolation problems with linear difference equations is pointed out.

This lecture will give the simple connection between the concept of polynomial spline functions and that of linear difference equations. It therefore yields some explanation of the well-known fact that in interpolation problems with splines one has to deal with matrices of band structure.


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    C. De Boor. On Calculating with B-Splines, J. Approximation Theory 6 (1972), 50–62.CrossRefzbMATHMathSciNetGoogle Scholar
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    H.B. Curry and I.J. Schoenberg. On Polya Frequency Functions IV: The fundamental Spline Functions and ther Limits. J. Anal. Math. 17 (1966), 71–107.CrossRefzbMATHMathSciNetGoogle Scholar
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    G. Meinardus. Bemerkungen zur Theorie der B-Splines. Symp. Public.: Spline-Funktionen, edit. By K. Böhmer, G. Meinardus, W. Schempp. Bibl. Institut Mannheim (1974), 165–175.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Günter Meinardus
    • 1
  1. 1.University of SiegenWest Germany

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