A note on the fitting of certain types of experimental data*

P. Wynn

Statistica Neerlandica, 1962, vol. 16, issue 2, 143-150

Abstract: Summary This paper is concerned with the problem of determining those values of the parameters Z, Aiαi (i = 1, 2, …, h) which provide a best fit of the form to the observed values fs= f(ts) (s = 1, 2, …, n) in the sense that the sum is a minimum. Two iterative numerical techniques for the solution of this problem are discussed. The first, a variable gradient method, converges rapidly but involves a relatively large amount of computation; the second involves less computation but converges less rapidly. It is shown that by application of a suitable acceleration technique to the second method, its convergence is made as rapid as that of the first. Samenvatting Dit artikel behandelt het probleem der bepaling van die waarden der parameters Z, Ai, αi (i = 1, 2,…, h), die de beste benadering geven van de vorm aan de waargenomen waarden fs= f(ts) (s = 1, 2, …, n) in die zin, dat de som een minimum is. Twee iteratief numerieke technieken voor de oplossing van dit probleem worden besproken. De eerste, een variabele gradient methode, convergeert snel, doch houdt een relatief groot aantal berekeningen in; de tweede houdt minder berekeningen in, doch con vergeert minder snel. Er wordt aangetoond dat, by toepassing van een geschikte versnellingstechniek by de tweede methode, de convergentie even snel is als die der eerste.

Date: 1962
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