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Frommer's nonlinear multisplitting methods for solving nonlinear systems of equations are extended to the asynchronous setting. Block methods are extended to include overlap as well. Several specific cases are discussed. Sufficient conditions to guarantee their local convergence are given. A numerical example is presented illustrating the performance of the new approach. 相似文献
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Parallel two-stage multisplitting methods with overlap for the solution of linear systems of algebraic equations are studied. It is shown that, under certain hypotheses, the method with overlap is asymptotically faster than that without overlap. Experiments illustrating this phenomenon are presented. 相似文献
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We show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M-matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC/860 hypercube are included. 相似文献
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