Numerical experiments demonstrate that reorderings improve convergence in nonsymmetric linear systems, suggesting effective preconditioning strategies.
Numerical experiments are presented whereby the effect of reorderings on the convergence of preconditioned Krylov subspace methods for the solution of nonsymmetric linear systems is shown. The preconditioners used in this study are different variants of incomplete factorizations. It is shown that certain reorderings for direct methods, such as reverse Cuthill--McKee, can be very beneficial. The benefit can be seen in the reduction of the number of iterations and also in measuring the deviation of the preconditioned operator from the identity.
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Benzi et al. (1999) studied this question.
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