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When preconditioning becomes a liability

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.