Control-Theoretic, Recursive Smoothing Splines

Interpolating or smoothing splines both require the inversion of a matrix of a size proportional to the total number of data points. This becomes a prohibitively costly proposition for large data sets and constitutes an inappropriate approach when the data is incremental or the underlying distribution from which the data is drawn is time-varying. In this paper, an algorithm is developed for the construction of recursive smoothing splines based on Calculus of Variations that can handle incremental and intermediate-sized batches of data sets, as well as data sets that are modified over time. The algorithm uses the previous data in the construction of the updated curve and a numerically efficient algorithm is developed to solve the problem.