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中文摘要：
该文通过比较几种迭代矩阵的谱半径,首次证明了经预条件子I＋S_α的IMGS迭代方法比经典的AOR迭代方法收敛速度快;其次证明了预条件SOR方法比经典的SOR方法收敛速度快.最后,证明了有关迭代矩阵的谱半径关于参数的单调性,改进了一些已知的结论.
英文摘要：
In this paper,by comparing with the spectral radiuses of the iterative methods,the authors prove,for the first time,that the IMGS method with the preconditioner I ＋ S_αis faster than the basic AOR iterative method,and then prove that the preconditioned SOR method is faster than the basic SOR method.Finally,the authors prove the monotony of the spectral radius with respect to the parameter and improve some recent known results.
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