Abstract
This paper presents a practical asymptotical optimal successive over-relaxation (SOR) method for solving the large sparse linear system. Based on two optimization models, asymptotically optimal relaxation factors are given, which are computed by solving the low-order polynomial equations in each iteration. The coefficients of the two polynomials are determined by the residual vector and the coefficient matrix A of the real linear system. The numerical examples show that the new methods are more feasible and effective than the classical SOR method.
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