Function minimisation using the Nelder and Mead simplex method with limited arithmetic precision: the self regenerative simplex

The behaviour of a curve fitting program is described which uses the Nelder-Mead simplex method to optimise the fit and which works with limited arithmetic precision. Apparent false minima are shown to be due to the creation of various simplex arrays which are regenerated unchanged by the logic of the process. A simple procedure is suggested for detecting the formation of such arrays and initiating restarting the search for the true minimum.