The two-stage iterative methods for symmetric positive definite matrices

摘要

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.