Numerische Mathematik

, Volume 47, Issue 1, pp 99–106

Smoothing noisy data with spline functions

  • M. F. Hutchinson
  • F. R. de Hoog

DOI: 10.1007/BF01389878

Cite this article as:
Hutchinson, M.F. & de Hoog, F.R. Numer. Math. (1985) 47: 99. doi:10.1007/BF01389878


A procedure for calculating the trace of the influence matrix associated with a polynomial smoothing spline of degree2m−1 fitted ton distinct, not necessarily equally spaced or uniformly weighted, data points is presented. The procedure requires orderm2n operations and therefore permits efficient orderm2n calculation of statistics associated with a polynomial smoothing spline, including the generalized cross validation. The method is a significant improvement over an existing method which requires ordern3 operations.

Subject Classifications

AMS(MOS): 65D 65K CR: G.1.2 G.1.1 

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • M. F. Hutchinson
    • 1
  • F. R. de Hoog
    • 1
  1. 1.CSIRO Division of Mathematics and StatisticsCanberraAustralia

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