代数多重网格方法的一个新的收敛性结果

A New Convergence Result for Algebraic Multigrid Method

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。

The interpolation operator is one of the important components of the algebraic multigric method （AMG）. In thi.s 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.