α-Diagonal Strictly Dominance Matrix and Convergence Theorem of SOR Iteration Method

For the linear equations system whose coefficient matrix is of α-diagonal strictly dominance or doubly α-chain diagonal strictly dominance,convergence properties of SOR iteration method are studied and some convergence theorems are given,which solves the problem of spectral radius of iterative matrices.Results obtained are applicable not only for α-diagonal strictly dominance matrix or doubly α-chain diagonal strictly dominance matrix,but also for generalized α-diagonal strictly dominance matrices.Finally,a numerical example is given for illustrating advantage of results.