Abstract
Some preconditioners [2, 3, 4, 5, 7, 8] have been reported to improve the convergence rate of the Gauss-Seidel method. However, these preconditioners do not influence the n-th row of a coefficient matrix. In the paper, we propose a new preconditioner (I+R) which acts on the n-th row. A convergence theorem and a comparison theorem of the proposed method are established. Numerical examples are also given.
