“The use of rational polynomials for approximating surfaces is investigated in this study. In particular, methods for estimating parameters for a rational polynomial model were investigated.
A method is presented for finding initial estimates of the parameters. Two iterative methods are discussed for improving those estimates in an attempt to minimize the sum of the squares of the residuals. These two methods are (1) Scarborough’s Method for applying the theory of least squares to nonlinear models and (2) the Method of Steepest Descent.
Data from two functions were chosen and approximated as illustrations. Each set of data was used two ways, (1) as generated, and (2) with random errors added, thus giving four examples.
Scarborough’s Method for improving the starting values was very effective, for the examples chosen, and the approximations were excellent. The study indicates, therefore, that rational polynomials have good potential as useful functions for surface approximants --Abstract, page ii
