Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 346230, 4 pages
http://dx.doi.org/10.1155/2013/346230
Research Article

An Autocorrelation Term Method for Curve Fitting

The Louisiana Accelerator Center, The University of Louisiana at Lafayette, Lafayette, LA 70504-4210, USA

Received 7 May 2013; Accepted 8 July 2013

Academic Editors: K. Djidjeli, J. Kou, and M. Qatu

Copyright © 2013 Louis M. Houston. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The least-squares method is the most popular method for fitting a polynomial curve to data. It is based on minimizing the total squared error between a polynomial model and the data. In this paper we develop a different approach that exploits the autocorrelation function. In particular, we use the nonzero lag autocorrelation terms to produce a system of quadratic equations that can be solved together with a linear equation derived from summing the data. There is a maximum of solutions when the polynomial is of degree . For the linear case, there are generally two solutions. Each solution is consistent with a total error of zero. Either visual examination or measurement of the total squared error is required to determine which solution fits the data. A comparison between the comparable autocorrelation term solution and linear least squares shows negligible difference.