【摘要】 McCormick多重网格收敛理论的基本假设的关键是存在一个与h无关且大于零小于1的常数,本文在光滑算子G_h为非亏损矩阵的条件下,证明了此常数与无后光滑部分的二重网格迭代收敛率是等价的,从而揭示了此常数的本质.并进一步指出Hackbush收敛理论的两大基本假设可为此常数存在的充分条件.最后分析了j—重网格(j>2)的粗网格迭代修正功能,据此以更简练的方法对多重网格迭代收敛率进行了估计,获得了类似文献的结果.更多还原

【Abstract】 The essential assumption of McCormick’s convergence theory ([2]—[4]) is that there is a constant a which is more than zero and less than one and independent of h. This paper proves that the constant is equivalent to the convergence rate of two-grid iteration without post smoothing if G_h is non-defect metrix, and that Hackbush’s two convergence assumptions~[1] can be acted as a sufficient condition of the constant a’s existence.Further more, the paper analyses the function of coarse-grid cornection of j-grid method(j is more than 2),which leads to a more clear mltigrid convergence analysis than[3].更多还原