An autocorrelation term method for curve fitting
type: Item
instance of: scholarly article
title: An autocorrelation term method for curve fitting
zbMATH Open document ID: 1298.65026
DOI: 10.1155/2013/346230
author: Louis M. Houston
published in: ISRN Applied Mathematics
publication date: 2014-11-11T00:00:00Z
review text: Summary: 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 \(2M\) 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.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 6368301
Wikidata QID: Q58994775
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/346230
OpenAlex ID: W2035378125
cites work: Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
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description: scientific article; zbMATH DE number 6368301