The direct method based on a fitting of distributions of semi-invariants

A new direct method (called TRYMIN) for phase-problem solution is described. At first a methodical procedure is presented for the construction of a direct method. The aim of the calculation is formulated as a consistency between theoretical and calculated distributions of invariants. A minimized function is obtained and an algorithm for its minimization is proposed. The algorithm is based on the partial decomposition of phases into three subsets and on the cyclical improvement of the estimate of local minima. The efficiency of the method has been tested on 23 structures and a short evaluation of the results of computer experiments with test structures is presented.