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Die probleem van die aanpassing van polinome aan ‘n reeks ewewydige gegewens

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  • T. E. W. Schumann

Abstract

The adjustment of polynomials to a series of equidistant data. If a quantity Ux has been observed for a set of equidistant values of x, and if we wish to adjust a polynomial to these data by the method of least squares, the coefficients kp can be computed in the form where the Ep(x) are functions of x and p, the values of which may be taken from a table. Tables for this purpose for 1 ≦ N ≦ 6 and for series of observations up to 50 were computed and edited by the Weather Bureau in Pretoria. In this paper formulae for the computation of the functions Ep(x) are deduced from the analogous development in orthogonal plynomials. In a final section the method is illustrated by a particular example, namely the representation of average air pressure as a function of geographical latitude.

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  • T. E. W. Schumann, 1950. "Die probleem van die aanpassing van polinome aan ‘n reeks ewewydige gegewens," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 4(3‐4), pages 158-167, June.
    • Handle: RePEc:bla:stanee:v:4:y:1950:i:3-4:p:158-167
    DOI: 10.1111/j.1467-9574.1950.tb00426.x
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