Technical Report CS0012

TR#:CS0012
Class:CS
Title: A STANDARD METHOD FOR SURFACE FITTING BY ORTHOGONAL POLYNOMIALS
Authors: E. Kantorowitz
PDFCS0012.pdf
Abstract: An algorithm for least squares fitting of a polynomial to a function z(x.y) of two independent variables is described. It is assumed that the function is given by a number of "measured values". which may be arbitrarily distributed over the XY plane. The polynomial is constructed as a linear combination of a set of polynomials which are orthonormalized over the set of given data points by the modified Gram Schmidt procedure. Formulas for the estimation of time and space required for the calculations and for the accuracy obtained are given. It is demonstrated that the method is numerically robust, that the costs of computations are reasonable, and that the procedure is suitable as a standard tool for least squares surface fitting. The experiments employed for the practical evaluation of the procedure are discussed.
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