Fitting control theoretic smoothing splines to very large data sets

In this dissertation we present several methods for fitting control theoretic splines to large data sets. In addition, we also present a method for fitting control theoretic splines to data sets containing position and derivative data. Applying control theoretic splines to a data set requires the inversion of matrices whose dimensions are the same as the number of data points in the data set. Methods for reducing the dimensions of the matrices are necessary if one wishes to fit a control theoretic spline to a large data set. Partitioning a data set or randomly selecting a small number of data points from the original set allow for the necessary reduction. Once the reduction is made there are several options for finding the optimal control function and optimal smoothed data needed to calculate the control theoretic spline.