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.
"Stochastic Interpretations and Recursive Algorithms for Spline Functions." Ann. Statist. 2 (4) 787 - 794, July, 1974. https://doi.org/10.1214/aos/1176342765