title: A comparison theorem for the iterative method with the preconditioner (I + S/sub max/)
abstract: A.D. Gunawardena et al. (1991) have reported the modified Gauss-Seidel method with a preconditioner (I + S). In this article, we propose to use a preconditioner (I + S/sub max/) instead of (I + S). Here, S/sub max/ is constructed by only the largest element at each row of the upper triangular part of A. By using the lemma established by M. Neumann and R.J. Plemmons (1987), we get the comparison theorem for the proposed method. Simple numerical examples are also given
keyphrases: comparison theorem iterative method preconditioner modified Gauss-Seidel method