Abstract
Relaxed technique is one of techniques for improving convergence rate of splitting iterative methods. Based on local relaxed method and system relaxed method of parallel multisplitting Frommer and Mayer [A. Frommer, G. Mayer, Convergence of relaxed parallel multisplitting methods, Linear Algebra Appl. 119 (1989) 141–152], we give the global relaxed parallel multisplitting (GRPM) method by introducing some relaxed parameters and study the convergence of our methods (GRPM-style) when the coefficient matrices are H -matrices. Numerical experiments show that, when choosing the approximately optimal relaxed parameters, our methods have faster convergent rate than the methods in Chang [D.W. Chang, Convergence analysis of the parallel multisplitting TOR methods, J. Comput. Appl. Math. 72 (1996) 169–177] Frommer and Mayer [A. Frommer, G. Mayer, Convergence of relaxed parallel multisplitting methods, Linear Algebra Appl. 119 (1989) 141–152]. Furthermore, the convergent and divergent rates of local relaxed parallel multisplitting (LRPM-style) methods about multislitting TOR, AOR, SOR, G-S, extraolated Jacobi methods as well as Jacobi iterative method are compared in detail.
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