document: A comparison theorem for the iterative method with the preconditioner -LRB- I + S/sub max / -RRB- A.D. Gunawardena et al. -LRB- 1991 -RRB- have reported the modified Gauss-Seidel method with a preconditioner -LRB- I + S -RRB- . In this article , we propose to use a preconditioner -LRB- I + S/sub max / -RRB- instead of -LRB- I + S -RRB- . 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 -LRB- 1987 -RRB- , we get the comparison theorem for the proposed method . Simple numerical examples are also given
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