Abstract: In order to improve the iterative solving speed of linear equations, a class of preconditioners are proposed and the convergence performance of the preconditioned AOR iterative methods with the proposed preconditioners is analyzed. The comparison results on the convergent speed between the AOR and the preconditioned AOR are obtained when the coefficient matrix is a strictly diagonally dominant Z-matrix. Meanwhile the comparison results for the multistage preconditioned methods are also given. The numerical example is provided to illustrate the obtained results.

Key words: preconditioner, preconditioned AOR iterative method, multistage preconditioned AOR iterative method, strictly diagonally dominant Z-matrix, spectral radius

摘要： 为了加快线性方程组的迭代法求解速度，提出了一类新预条件子，分析了相应的预条件AOR迭代法的收敛性。给出了当系数矩阵为严格对角占优的Z-矩阵时，AOR和预条件AOR迭代法收敛速度的比较结论。同时也给出了多级预条件迭代法的相关比较结果，推广了现有的结论。数值算例验证了文中结果。

关键词: 预条件, 预条件AOR迭代法, 多级预条件AOR迭代法, 严格对角占优Z-矩阵, 谱半径