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On Interpolation by Spline Functions and its Minimal Properties

  • I. J. Schoenberg
Part of the Contemporary Mathematicians book series (CM)

Abstract

Polynomials are wonderful even after they are cut into pieces, but the cutting must be done with care. One way of doing the cutting leads to the so-called spline functions. These were introduced by the writer in 1944 as a tool for the approximation of functions and were suggested by the work of T. N.E. Greville and other actuarial writers on the subject of osculatory interpolation (for the connections and references see [8], Part B). The other tool used was the law of the flow of heat in a homogeneous wire and with both tools combined extensive ballistic tables were approximated and thereby smoothed (see [8]). For recent largescale physical applications of cubic spline functions see [6]. The spline functions used in [8] had equidistant knots. In 1945 H. B. Curry and the author wrote a paper on spline functions with arbitrarily spaced knots which for no good reason remained unpublished (see the Abstract [2]). For further work on spline functions and related topics see the list of references which claims no completeness.

Keywords

Spline Function Spline Interpolation Interpolation Problem Minimal Property Divided Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • I. J. Schoenberg
    • 1
  1. 1.The Institute for Advanced StudyThe University of PennsylvaniaUSA

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