Comparison theorems of preconditioned Gauss–Seidel methods for M-matrices

摘要

In this paper, a new preconditioner for the Gauss–Seidel method is proposed for solving linear systems whose coefficient matrix is an M-matrix. Several comparison theorems are shown for the proposed method with several preconditioners. It follows from the comparison results that our preconditioner is one of the best preconditioners in the sense of convergence rate. Finally, numerical examples are given to illustrate our theoretical results. Two conjectures are proposed as well based on our numerical tests.