A comparative study of minimization methods in the fitting of alpha-particle spectra

Three methods of numerical optimization (Levenberg—Marquardt, Fletcher and Davidon—Fletcher—Powell) and two minimization criteria (Neymanʹs and maximum likelihood chi-square) have been tested to evaluate their performance in the fitting of alpha-particle spectra. High-resolution reference spectra of 243Am and 239Pu have been analysed. Results indicate that the method of Powell, a minimization procedure which does not require the evaluation of derivatives, in preferable when no previous information about spectra is available. On the other hand, the Levenberg—Marquardt method is very efficient when approximate values of all peak parameters are known.