Knot Selection for Least Squares Thin Plate Splines

An algorithm for selection of knot point locations for approximation of functions from large sets of scattered data by least squares Thin Plate Splines is given. The algorithm is based on the idea that each data point is equally important in defining the surface, which allows the knot selection process to be decoupled from the least squares. Properties of the algorithm are investigated, and examples demonstating it are given. Results of some least squares approximations, are given and compared with other approximation methods. ', .. 1