H-Splittings and two-stage iterative methods

SummaryConvergence of two-stage iterative methods for the solution of linear systems is studied. Convergence of the non-stationary method is shown if the number of inner iterations becomes sufficiently large. TheR1-factor of the two-stage method is related to the spectral radius of the iteration matrix of the outer splitting. Convergence is further studied for splittings ofH-matrices. These matrices are not necessarily monotone. Conditions on the splittings are given so that the two-stage method is convergent for any number of inner iterations.

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