Two fast methods of superposing two sets of atomic coordinates by least-squares refinement are described and related to two earlier fast methods. A Newton method is applied to rotations of a 3 x 3 outer product matrix used previously by Ferro & Hermans [Acta Cryst. (1977), A33, 345-347] and by McLachlan [Acta Cryst. (1972), A28, 656-657]. Three of the methods work better if one molecule has its inertial matrix aligned with xyz. A Newton-Gauss method that rotates the coordinates can converge rapidly after a rough orientation using three strategic atoms. The average superposition takes about 0.003 s on a Cyber 175 with the best method, rotations about the xyz axes in turn. Experience with reliability is reported for large residuals.
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C. E. Kenknight (1984) studied this question.