Abstract
The use of simulated annealing procedures in connection with the matrix method and a matrix-tree algorithm is proposed to obtain a model-free fit of the scattering density profile from a given experimental neutron reflectivity curve. Due to the ill-defined nature of the phaseless Fourier transform problem, multiple minima and ambiguities exist. Simulated annealing procedures make it possible to overcome barriers and local minima during a fit since with a certain probability also those variations are accepted during the minimization procedure which do not improve the fit
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