Efficient Polynomial Preconditioning for the Conjugate Gradient Method
Efficient Polynomial Preconditioning for the Conjugate Gradient Method
复制标题
共轭梯度法的高效多项式预处理
DOI：
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发表时间：
1990
影响因子：
3.1
通讯作者：
C. Vaughan
中科院分区：
文献类型：
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作者：
S. Eisenstat;J. Ortega;C. Vaughan
本文阐述并比较了在共轭梯度法中进行m步或多项式预处理时减少计算量的步骤。这些程序是基于Bank和Douglas给出的相应的一步预处理程序。诺默。数学，1(1985)，第489-492页]，Conrad and Wallach[Numer.数学，27(1979)，第371-372页]，和Eisenstat[SIAM J.Sci.统计学家。Comput.，2(1981)，pp.1-4]，并特别适用于SSOR预适应。基于运算计数、存储、并行和向量特性进行了比较，得出结论：Eisenstat过程是最有效的。并给出了在并行计算机上的数值实验结果。
This paper formulates and compares procedures for reducing computation in carrying out m-step or polynomial preconditioning in the conjugate gradient method. These procedures are based on corresponding ones for one-step preconditioning given by Bank and Douglas [Appl. Numer. Math., 1(1985), pp. 489–492], Conrad and Wallach [Numer. Math., 27 (1979), pp. 371–372], and Eisenstat [SIAM J. Sci. Statist. Comput., 2 (1981), pp. 1–4], and apply, in particular, to SSOR preconditioning. Comparisons are made based on operation counts, storage, and parallel and vector properties, and it is concluded that the Eisenstat procedure is the most effective. Numerical experiments on a parallel computer are also given.