TELS - LEAST-SQUARES SOLUTION OF THE STRUCTURE-INVARIANT EQUATIONS

Procedures are described to extract the values of individual phases from estimated structure invariants. The linear-equation and least-squares methods are used as two separate techniques in these procedures. The linear-equation method uses a linearly independent set of equations, with arbitrarily assigned integers, which are sufficient in number to solve for values of an equal number of phases. The least-squares method uses a set of overdetermined equations in which an 'integer problem' has to be considered. The assembly of these two techniques with a novel integer-trial-and-error method shows a remarkable ability to overcome the 'integer problem'. As a test of the whole procedure, phases were extracted from three-phase structure invariants calculated from the theoretical data for the platinum chloride derivative of cytochrome c550.