Used to be: Coordinates accuracy

[Howard Flack]

Lynn,

   In some of my spare moments (so few), I think about the presentation
you made at the computing school in Western Washington with the 
analysis of eigenvalues and vectors of the normal-equations matrix for 
macromolecular refinements. One thing that bothers me is that the 
eigenvalue spectrum can be changed by  making a linear transformation 
of the variables from x(i) to s(i)x(i) where s(i) is an arbitrary 
scale factor. [You can also instead of 'refining on |F(h)|' refine on
k(h).|F(h)| where k(h) is some arbitrary scale factor for each
reflection. As the weights transform inversely to |F|^2^, this has no
effect on the eigenvalues.] I would not expect the real nature of the
refinement to be altered by such a silly trick but one can nevertheless
easily arrange for all the eigenvalues to have the same value. This
seems to suggest that the eigenvalues are not the invariants that one
needs to examine or may be I am talking utter nonsense?

Best wishes,
    Howard

-- 
Howard Flack        http://www.unige.ch/crystal/ahdf/Howard.Flack.html
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