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A method for greatly improving the efficiency of numerical procedures for solving the fundamental equations of the statistical geometric method [Wilkins, Varghese & Lehmann (1983). Acta Cryst. A39, 47-60] is presented. The method involves optimizing the step length in a one-dimensional search based on two trial solutions. For constraint functions, fr, which have derivatives fr, j1 = ∂fr/∂pj, which are linear in p, it is shown that the one-dimensional search does not involve any additional Fourier transforms (i.e. lengthy computations).