A Fast Algorithm for Smoothing Data on a Rectangular Grid while Using Spline Functions

An efficient computational method is presented for fitting a bivariate spline function to a set of measured data on a rectangular grid. The coefficients in the B-spline representation of this spline are obtained by the solution of a linear system which can be arranged in a matrix form, conformable withthe Kronecker product of two band matrices of small size and bandwidth. The number of knots of the spline and their positions are determined automatically. Instead the algorithm expects a parameter to control the tradeoff between closeness of fit and smoothness of fit.