In this paper, we inquire into the fact that coef fi cient matrix is the convergence of iteration methods for solving the system of e quations with quasi-diagonally dominant matrix, and set the convergent condition s for Jacobi iteration method, G-S iteration method and SOR method for solving t he system of equations with quasi-diagonally dominant matrix.

G-S iteration method is a classical method for large scale sparse matrix equations.

The present paper discusses the convergence of SOR iterative method for solving the linear system when the ratio matrix is a nonsingular square matrix and puts forward some principles to judge the convergence of SOR iterative method.

Estimate for error of the AOR iterative method;

Preconditioned parallel AOR iterative method;

A new estimate of error of AOR iterative method

In this paper we prove that the AOR iteration matrix Lr,ω(with ω>0 and r≠0) of A converges iff0<ω<2 1+α2,ω+ω-2 α2<r<1 2[ω+(2-ω)2 ωα2],r≠0,or equivalently,{r≥rb,0<ω<2+rα2-αr2α2+4r-4 1+α2;rb≥r>-2 α2,r≠0,0<ω<2+rα2 1+α2,where rb=2 1+1+α2.