Abstract
Two-stage iterative methods for the solution of the symmetric positive definite linear system Ax= b are considered. In this paper, in particular: strong conditions and feeble conditions on splittings are given so that the two-stage methods are convergent for any number of inner iterations and for any nonnegative even number of inner iterations, respectively. Some suitable examples of strong P-regular splittings are presented and the convergence of some feasible two-stage methods is discussed, in which the outer splitting is weak P-regular and the inner splitting is strong or weak P-regular splittings.
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