Discrete polynomial spline approximation methods

  • Tom Lyche
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 501)


Discrete splines were introduced by Mangasarian and Schumaker [12] as solutions to certain minimization problems involving differences. They can be defined as piecewise polynomials where the ties between each polynomial piece involve continuity of differences instead of derivatives. We study discrete analogs of local spline approximations, least squares spline approximations, and even order spline interpolation at knots. Error bounds involving differences over a finite number of points are given in each case. These contain classical error bounds as a special case.


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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Tom Lyche
    • 1
  1. 1.Department of MathematicsUniversity of OsloOsloNorway

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