New convergence results for alternating methods

The alternating methods for solving the large system of linear equations Ax=b are investigated. The convergence and the monotone convergence theories for the alternating method are formulated when the coefficient matrix is an H-matrix or a monotone matrix. Sufficient conditions are established for the induced splitting by the alternating method to be a regular splitting. Furthermore, new comparison theorems which improve previous comparison theorems are proved and several concrete applications are given.