A Smooth Fitting Based on a Generalized Inverse Theory

Abstract

A Generalized inverse theory is applied to a multivariate smooth fitting for irregularly spaced data. A smoothing function is expanded with cubic B-spline basis with equally spaced dense knots. Their coefficients are obtained by a least squares procedure using the a priori ioforrnation that the first and the second derivatives of the function are everywhere zero Plus random errors. The method is also regarded as an FEM approximation of a lateral deformation of an elastic bar or plate which is under tension and is pulled to data points by springs.