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Title: Curve-fitting according to the method of A. Ekke and R. Schmidt (1) ; An iterative method for approximating to the roots of a polynomial (2)
Author: Sealy, E. H.
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1940
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When fitting a curve to a given set of data, it is usual, having chosen the curve-type which will best suit the data, to take as abscissae for the plotted points of the curve the observations themselves, and then 'smooth' the frequencies or weights of these the correct ordinates, as if considering these frequencies to be subject to 'error' but the points at which the observations were made to be exact. In the present method, however, we intend to make use of the inverse process. That is, we work as if considering the frequencies to be exact, but the observations to be in error. Thus we make no alteration in the frequencies as they are presented to us, but combine two processes for 'smoothing' the observations as follows: (i) We take, as our abscissae, not the given observations, but a certain set of points calculated from the frequencies and the chosen curve-type which have been called 'Ekke's Best Values', after some work done by A. Ekke in connection with them in a Kiel dissertation, 1934. (ii) We now further smooth these abscissae to as close an approximation to the given observations as is required, by combining the given observations in a set of polynomials with coefficients to be determined (a process suggested by R. Schmidt in an article appearing in the Annals of Mathematical Statistics , Vol.v , P.30).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available