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Convergence property of the successive over-relaxation (SOR) method depends on a relaxation parameter whose optimal value can be hardly computed. This paper determines the optimal value under a minima...l condition for an intermediate residual in the successive computation of the SOR method. Through the organizations of formulas, the authors eliminate the relaxation parameter and propose a new iterative solver: successive minimal residual (SMR) method. Numerical tests for over 700 practical and real nonsymmetric matrix problems comparably check the performances of convergence, computation time and accuracy for the SMR method and other classical iterative methods.show more
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