On Best Approximations of Linear Operators

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


We recently gave in the note [8] some applications of the so-called spline interpolation formula to real variable theory. The purpose of the present note is to point out the fundamental role of spline interpolation in the numerical analysis of functions of one real variable. The role which spline interpolation is here called upon to play is based on the ideas of A. Sard [4, 5] and is inherently due to the two familiar requirements for approximation formulae of numerical analysis: 1) That they be linear, 2) That they be exact for polynomials of a certain specified degree.


Spline Function Spline Interpolation Approximation Formula Minimal Property Interpolation Formula 
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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • I. J. Schoenberg
    • 1
  1. 1.Institute for Advanced StudyUniversity of PennsylvaniaUSA

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