The two-stage arithmetic mean method

In several recent works, the Arithmetic Mean Method for solving large sparse linear systems has been introduced and analysed. Each iteration of this method consists of solving two independent systems. When we obtain two approximate solutions of these systems by a prefixed number of steps of an iterative scheme, we generate an inner/outer procedure, called Two-Stage Arithmetic Mean Method. General convergence theorems are proved for M-matrices and for symmetric positive definite matrices. In particular, we analyze a version of Two-Stage Arithmetic Mean Method for T(q, r) matrices, deriving the convergence conditions. The method is well suited for implementation on a parallel computer. Numerical experiments carried out on Cray-T3D permits to evaluate the effectiveness of the Two-Stage Arithmetic Mean Method