The test algorithm and the quasi-optimum factor of SSORPCG. Based on the condition that the symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient method (namely, SSORPCG) is relatively insensitive to the exact choice of the relaxation factor, this paper provides a test algorithm to predict the quasioptimum relaxation factor for SSORPCG of the corresponding large linear system by analyzing and testing the small size problems. The quasi-optimum relaxation factor leads to the almost optimum convergence speed. Meantime, the algorithm avoids the difficulty in seeking the optimum relaxation factor in theory. Numerical experiments are presented to verify the efficiency of the algorithm. Finally, it is proved from both theory and experiments that the quasi-optimum relaxation factor defined by the test algorithm is accurate to the kind of problem with the optimum relaxation factor irrelated to the scale.

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