Examination of different nonlinear algorithms for X-ray processing with personal computers

Different nonlinear Least Square Methods (LSM) for processing X-ray spectra with microcomputers are studied. Gaussian shape for the X-ray lines is accepted. The model function p for the description of a spectral region is constructed and iterative methods for minimizing the functional Χ2 = Φ(p) are applied. The following nonlinear LSM have been used: steepest descent method, Fletcher-Reeves method, Davidson-Fletcher-Powell method, the Marquardt algorithm and the Hooke-Jeeves pattern search method. Programs using these algorithms have been written in BASIC and their rate of convergence has been checked processing two regions of the same spectrum. One region comprises the Mn-Kα, Mn-Kβ, Fe-Kα and Fe-Kβ peaks and the second region - Cu-Kα, Cu-Kβ and Zn-β peaks. The reproducibility of the different algorithms has been studied. The conclusion has been drawn that for the purposes of energy dispersive X-ray fluorescence analysis the most reliable program for spectra processing is the one based on the Marquardt algorithm. The results obtained in this way are independent of the power of the polynomial used to approximate the background. Line intensity ratios have to be introduced in the model function when processing spectra with low counting statistics. 5 figs., 5 tabs., 20 refs