Fast Compact Algorithms and Software for Spline Smoothing
This is an item in the Springer Briefs in computer science. In the Springer Briefs series, the idea is to give short (50-125 pages) reports on a hot topic or a timely snapshot, or an in-depth study of a special case etc. The publication should be self contained and easy to prepare. These issues are primarily intended for rapid electronic publication.
The present volume has only 45 pages and presents several (fully listed) matlab scripts of different methods to compute cubic spline smoothers of a set of measurements of a one-dimensional signal. Smoothing is obtained via estimating a noise level using GCV (generalized cross validation) and choosing an optimal relaxation parameter to get a balance between smoothness and fitting of the data. The numerical implementations are based on a dedicated Cholesky solver, QR factorization, or Fourier transforms. These are used for continuous spline smoothing (the integral of the square of the second derivative is minimized), but Cholesky and Fourier methods are also rewritten for discrete spline smoothing (the integral is replaced by a discrete sum).
For each script, a Monte Carlo simulation tests and compares the method for efficiency, so that the most efficient one can be identified.
The booklet contains a short, practical description of the algorithm and the full listing of the scripts, but one may be more interested in having the software as well, instead of retyping everything. However, neither at the Springer website nor at the author's website could I find a place to download it.