一类改进的高斯-赛德尔迭代法的比较性定理

A New Comparison Theorem for the Preconditioned Gauss-Seidel Iterative Method

讨论了改进的高斯-赛德尔迭代法的收敛性.若系数矩阵为非奇异不可约M?矩阵,则该预条件下高斯-赛德尔迭代法收敛的快慢取决于原高斯-赛德尔迭代法谱半径的大小.同样,在该预条件下高斯-赛德尔迭代法的谱半径大小与其他高斯-赛德尔迭代法的谱半径大小有关.

In this paper, the convergence analysis for a new preconditioned method was discussed. If the coefficient matrix is a nonsingular irred convergence rate of this iterative method depends on the spectral radius of the method. Likewise, the spectral radius of the preconditioned Gauss-Seidel Gauss-Seidel iterative ucible M-matrix, the original Gauss-Seidel iterative method also depends on one of the preconditioned Gauss-Seidel methods. Finally, some numerical examples are given to explain our theoretical results.