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An efficient method for calculating smoothing splines using orthogonal transformations

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Summary

A procedure for calculating the mean squared residual and the trace of the influence matrix associated with a polynomial smoothing spline of degree 2m−1 using an orthogonal factorization is presented. The procedure substantially overcomes the problem of ill-conditioning encountered by a recently developed method which employs a Cholesky factorization, but still requires only orderm 2 n operations and ordermn storage.

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Authors and Affiliations

  1. CSIRO Division of Mathematics and Statistics GPO, Box 1965, 2601, Canberra, ACT, Australia

    F. R. de Hoog & M. F. Hutchinson

Authors
  1. F. R. de Hoog
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  2. M. F. Hutchinson
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de Hoog, F.R., Hutchinson, M.F. An efficient method for calculating smoothing splines using orthogonal transformations. Numer. Math. 50, 311–319 (1986). https://doi.org/10.1007/BF01390708

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