Knowledge Bank

In this paper a new fitting algorithm is discussed which works with Voight functions. The fitting algorithm used is an extension of the rapidly convergent gradient method of Fletcher and $Powell1$ who claim faster convergence than the Newton-Raphson method which has been used by Chang & $Shaw2$ for fitting Lorentz line widths. The Fletcher and Powell algorithm involves the effects of second derivatives although second derivatives are not explicitly calculated. In our algorithm first and second derivatives are computed not numerically, but analytically via a modification to Drayson’s Voight functions $subroutine.3$ This algorithm provides rapid convergence even when there are few date points. Profiles have been fitted with as few as 5 date points. Our typical line fits involve 40 points. The run time of the algorithm has been compared with the shrinking cube algorithm of $Hillman4$ and found to be a least 10 times faster under identical starting conditions. Sample single line and double line fits are shown illustrating the speed and efficiency of the new algorithm.