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The Computer Journal 1960 2(4):170-173; doi:10.1093/comjnl/2.4.170
© 1960 by British Computer Society
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Curve Fitting with a Digital Computer

C. W. Clenshaw

National Physical Laboratory, Teddington, UK

Forsythe (1957) has described a method for fitting polynomials to a set of points, using the principle of least squares. The method, designed to exploit the advantages of high-speed computers, uses orthogonal polynomials to overcome the problems of ill-conditioning which are usually associated with this approach. The present paper shows how this powerful method can be modified to save a substantial proportion of the machine storage. This is achieved by representing each polynomial within the machine by the coefficients in its Chebyshev series.


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