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Theoretically, preconditioning does not reduce the number of iterations
required for an exact solution,
but it gets us closer quicker;
so,
we may hope to omit all the work of the later iterations.
Surprisingly and unfortunately,
several of my colleagues have observed
later iterations in which preconditioning actually slows convergence.
Then,
we are better off reverting to
the nonpreconditioned initial form.
Sorry, but I am unable to offer guidance
or any method to cope with this issue
other than your own application-dependent experimentation.

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2015-05-07