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Oscillation matrices with spline smoothing

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Summary

Spline smoothing can be reduced to the minimization of a certain quadratic form with positive semidefinite matrix. For polynomial splines this matrix is closely related to an oscillation matrix and its eigenvectors show the typical sign distribution. This fact is the basis for a variant of spline smoothing.

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Authors and Affiliations

  1. Leibniz Rechenzentrum der Bayer. Akademie der Wissenschaften, Barerstr. 21, D-8000, München 2, Bundesrepublik Deutschland

    A. Demmler &  C. Reinsch

Authors
  1. A. Demmler
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  2. C. Reinsch
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Additional information

This author is pleased to acknowledge support from the National Science Foundation (U.S.A.) under Grant Number GJ-29988X.

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Demmler, A., Reinsch, C. Oscillation matrices with spline smoothing. Numer. Math. 24, 375–382 (1975). https://doi.org/10.1007/BF01437406

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  • DOI: https://doi.org/10.1007/BF01437406

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