In this paper, we prove the hγ,ω (0≤γ≤ω<c,ω>0) minimum is the h1,1, here, hγ,ω is an error estimate constant of the AOR method s error estimate formula in strictly diagonally dominant matrix.

In this paper, the spectral radius ρ(G)=ρ(L 1,1 ) of the iterative matrix G=L 1,1 of Gauss-Seidel method being the minimum of ρ(L r,w ) (0≤r≤w≤1, w>0) are proved under the condition that B=L+U≥0,ρ(B)<1 for the Jacobi iterative matrix B of the linear systems coefficient matrix A, that is Gauss-Seidel iteration being the fastest convergent iterative method in the AOR method.

Estimate for error of the AOR iterative method;

Preconditioned parallel AOR iterative method;

A new estimate of error of AOR iterative method

Given two-stage iteration,a comparison was drawn between spectral radii of AOR and preconditioned AOR methods,aiming at more accurate results of R1-factor of the outer iteration of two-stage iterative.

Firstly, we obtain new bound of the iteration matrix, then we analyze the convergence of AOR method.

In this paper,the parallel AoR algorithm for the solution of a large set of linear equa-tions with positive definite Hermitian coefficient matrix is investigated, and the convergance theorem of the parallel AoR algorithm is proved under the assumption that the matrix A is in the dissected form.