代数多重网格方法的一个新的收敛性结果

插值算子是代数多重网格方法(AMG)的重要构成组元之一,为此提出了构造AMG方法插值算子新的、更具有一般性的方法。通过对矩阵范数的估计证明了其收敛性。该方法给出了经典AMG方法插值公式的统一描述,推广了AMG方法的应用范围。最后指出该结果在某些情形下可以应用于多水平不完全LU分解法(ILUM),为进一步证明一般ILUM方法的收敛性提供了思路。

A New Convergence Result for Algebraic Multigrid Method

The interpolation operator is one of the important components of the algebraic multigric method(AMG).In this paper,the author proposes a new and general way to construct the interpolation operators for AMG methods. By estimating the norms of the related matrices,the author proves the convergence of the new method.This method gives a uniform expression of the classic AMG interpolation operators and extends the range to use AMG.At last,the author point out that our result can be applied to the multi-elimination incomplete LU(ILUM) method in some special cases,and this supplies some idea to prove the convergence of ILUM in general cases.