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 Results for DC.creator="H." AND DC.creator="A." AND DC.creator="Hauptman" in section 16.1.4 of volume F
Parameter shift
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.4.3, p. 418 [ doi:10.1107/97809553602060000850 ]
... be used to minimize by varying the phases. So far, a seemingly simple algorithm, known as parameter shift (Bhuiya & Stanley, 1963 ... to reduce the value of the minimal function. For example, a typical phase-refinement stage consists of three iterations or scans through the reflection list, with each phase being shifted a maximum of two times by 90° in either the ...

The minimal function
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.4.2, pp. 417-418 [ doi:10.1107/97809553602060000850 ]
... an objective function like the minimal function, (Debaerdemaeker & Woolfson, 1983; Hauptman, 1991; DeTitta et al., 1994), provides an alternative approach to phase refinement or phase expansion. is a measure of the mean-square difference between the values of the triplets calculated using a particular set of phases and the expected values of ...

The tangent formula
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.4.1, p. 417 [ doi:10.1107/97809553602060000850 ]
... tangent formula 16.1.4.1. The tangent formula The tangent formula, (Karle & Hauptman, 1956), is the relationship used in conventional direct-methods programs to compute given a sufficient number of pairs () of known phases. It can also ... portion of the dual-space Shake-and-Bake procedure (Weeks, Hauptman et al., 1994; Usón & Sheldrick, 1999). The ...

Reciprocal-space phase refinement or expansion (shaking)
Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I.  International Tables for Crystallography (2012). Vol. F, Section 16.1.4, pp. 417-418 [ doi:10.1107/97809553602060000850 ]
... shaking) 16.1.4. Reciprocal-space phase refinement or expansion (shaking) Once a set of initial phases has been chosen, it must be ... invariants whose values are presumed known. In theory, any of a variety of optimization methods could be used to extract phase ... shift optimization of the minimal function, and maximization of Karle-Hauptman determinants (Section 16.1.12.7). 16.1.4.1. The tangent formula | | The ...

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