H-SPLITTINGS AND 2-STAGE ITERATIVE METHODS

Convergence 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. The R1-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 of H-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.