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What is the state-of-the-art in the efficient computation of smoothing splines?

The algorithm I see mentioned most often is that of Reinsch, dating back to 1967. As I understand it, the most expensive part is performing a Cholesky decomposition. What other algorithms for smoothing splines have there been since then?

alang
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A bit more modern than what you quote is de Boor, C. (1978) A Practical Guide to Splines, Springer Verlag. An efficient algorithm for smoothing splines is given by Hutchinson, M.F. and de Hoog, F.R. (1985) Smoothing Noisy Data with Spline Functions, Numerische Mathematik, 47, p. 99-106 (see also Hutchinson, M.F. (1986) Cubic Spline Data Smoother, Transactions on Mathematical Software, vol. 12, 150-153; you will find the FORTRAN source of the algortihm in http://calgo.acm.org).

Note also that the Kalman filter can be a good tool to fit some types of splines; see for instance an answer I gave sometime ago on Kalman filter vs. smoothing splines. You will find much relevant information if you search here in CrossValidated using "splines" as a tag.

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F. Tusell
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  • Thanks for your answer. As far as I can tell, the algorithm in _A Practical Guide to Splines_ is the same as the one given by Reinsch. I haven't yet looked at your other reference. Regarding Kalman filters, I believe they would require additional structure, such as knowledge about transitions between data points. – alang May 20 '12 at 10:29