On the application of phase relationships to complex structures. XXIX. Choosing the large Es

The set of large Es through which a structure is solved by direct methods is usually chosen by a convergence or convergence-divergence process. This process aims to give a strong phase-extension pathway starting from a small set of Es whose phases are known or allocated in some way. Sometimes sets of reflexions thus obtained are poorly conditioned and under tangent-formula refinement even initially correct phases will degenerate to randomness. A simple new algorithm has been developed which improves the conditioning of the complete set of reflexions and their relationships and is more appropriate to current trends to start refinement from a complete set of random phases. A particular feature of this algorithm is that it maximizes the minimum number of relationships for any reflexion.