A COMPARISON OF OPTIMIZATION METHODS FOR FITTING CURVES TO INFRARED BAND ENVELOPES

Abstract

A comparison has been made of seven numerical methods of fitting infrared absorption band envelopes with analytical functions using nonlinear least squares approximations. Gauss and Cauchy (Lorentz) band shape functions are used, and also sum and product combinations of the two. The methods have been compared with respect to both the degree of convergence and to the computation time needed to achieve an acceptable fit.The most effective method has matched the overlap envelope of a steroid spectrum containing 16 bands; this necessitated the optimization of 65 variables. More complex spectra can be dealt with by a "moving subspace" modification in which only the parameters of a group of adjacent bands are adjusted at one time. Automatic computer programs have been written for five of the methods, and for the moving subspace modification. These will be published elsewhere.If the computed curve is convoluted with the spectral slit function before making the least squares calculations, the distortion of the observed spectrum caused by the finite spectral slit width can be corrected. In some cases this method of diminishing the slit distortion is better than direct methods, particularly when dealing with strongly overlapped bands.