Stochastic Interpretations and Recursive Algorithms for Spline Functions

Abstract

Spline functions, which are solutions to certain deterministic optimization problems, can also be regarded as solutions to certain stochastic optimization problems; in particular, certain linear least-squares estimation problems. Such an interpretation leads to simple recursive algorithms for interpolating and smoothing splines. These algorithms compute the spline using one data point at a time, and are useful in real-time calculations when data are acquired sequentially.