Incomplete Cholesky and its modified variant provide the largest work reduction among black-box preconditioners for CG, but fail on roughly 20% of problems, and AMD matrix ordering substantially outperforms RCM.
T.George, A.Gupta, and V.Sarin.An em- pirical analysis of the performance of precondi- tioners for spd systems
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An Empirical Study of Conjugate Gradient Preconditioners for Solving Symmetric Positive Definite Systems of Linear Equations
Incomplete Cholesky and its modified variant provide the largest work reduction among black-box preconditioners for CG, but fail on roughly 20% of problems, and AMD matrix ordering substantially outperforms RCM.