An Autocorrelation Term Method for Curve Fitting. (24th July 2013)

• Record Type: Journal Article
• Authors: Houston, Louis M.
• Other Names: Djidjeli K. Academic Editor.; Kou J. Academic Editor.; Qatu M. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2013(2013)
• Publication Date: 2013-07-24
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.1155/2013/346230
• Languages: English
• ISSNs: 2090-5564

Abstract

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 2 M solutions when the polynomial is of degree M . 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.