线性方程组预条件AOR迭代法的一些改进结果

摘要

In this paper,we provide more comparison theorems on preconditioned AOR iterative method with preconditioner I＋βU for solving linear systems. Some recent results are improved. Comparison results and the numerical example show that the rate of convergence of the preconditioned Gauss-Seidel method is faster than that of the preconditioned AOR iterative method.%本文运用I＋βU作为预条件矩阵，讨论了预条件AOR迭代法的收敛性和谱半径的比较结果，并且改进了文[1]中的有关结果．理论和数值试验都表明了当0≤r≤ω≤s1时，预条件Gauss—Seidel迭代法要优于预条件AOR迭代法．