Accurate least-squares techniques using the orthogonal function approach

Sullivan, Jerry

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Accurate least-squares techniques using the orthogonal function approach

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Accurate least-squares techniques using the orthogonal function approach

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Personal Author:

Sullivan, Jerry
Corporate Authors:

United States. Environmental Data and Information Service. ; Center for Environmental Assessment Services (U.S.)

United States. Environmental Data and Information Service. ; Center for Environmental Assessment Services (U.S.) Less -
NOAA Program & Office:

NESDIS (National Environmental Satellite, Data, and Information Service)
Description:

With the increased availability of computers, the least-squares method of analyzing data is now widely used. This report presents the orthogonal function approach to the least-squares method. This approach is important in practice because it provides accurate numerical results, even when used on large data sets. It is also useful in theoretical considerations, particularly in examining the statistical structure of a data set. The Gram-Schmidt orthogonal function approach is first compared to the standard least- squares method. Next, properties of the approach are shown and a technique to enhance its numerical accuracy is given. Statistical aspects are then discussed. Some applications of the approach are illustrated. The first use can be described as a dominant pattern recognition technique for large data sets and the second is for time series analysis. Finally, a time-saving method used when the functions fitted to the data are polynomials is described, and a related application to Fourier analysis is included.
Keywords:

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Computer Programs Least Squares
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NOAA technical report EDIS ; 33
Document Type:

Technical Report
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Public domain
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Library
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urn:sha256:15900cb08d181a0ebbb9479fe7970b5f6e5d7c2cb4d5c1cf501b66995240a9bd
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https://repository.library.noaa.gov/view/noaa/30831/noaa_30831_DS1.pdf
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Accurate least-squares techniques using the orthogonal function approach

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