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#### An alternative method of solving the layer scaling equations of Hamilton, Rollet, and Sparks

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##### Citation

Fox, G. C., & Holmes, K. C. (1966). An alternative method of solving the layer
scaling equations of Hamilton, Rollet, and Sparks.* Acta Crystallographica A,* *20*,
886-891. doi:10.1107/S0365110X66002007.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0019-B1DC-D

##### Abstract

The relationship between the methods of Dickerson (1959), Rollett & Sparks (1960), and Hamilton,
Rollett & Sparks (1965) (HRS) is discussed, together with a short account of why the first two methods
are unsatisfactory. An alternative iterative method (the method of 'shortest path') of solving the layer
scaling equations of HRS is given which converges faster than the solution given by HRS. An exact
solution of the equations of HRS is given which may be applied to situations where a simple weighting
scheme may be used. The method of 'shortest path' may be important in protein crystallography where
setting up the normal matrix may mean scanning 100000 reflexions and therefore the speed of convergence
is of paramount importance