Parallel algorithms for the solution of certain large sparse linear systems
Parallel algorithms for the solution of certain large sparse linear systems
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DOI：
10.1080/00207168408803441
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发表时间：
1984
影响因子：
1.8
通讯作者：
M. Benson;J. Krettmann;M. Wright
中科院分区：
文献类型：
--
作者：
M. Benson;J. Krettmann;M. Wright
提出了几种近似反演技术，它们为求解由边值问题的离散化引起的线性系统的几种迭代方法提供了并行增强。特别是，雅可比、高斯-赛德尔和连续的过松弛方法可以通过所考虑的扩展在并行环境中得到显着改进。给出了一个特殊情况的收敛证明。检查了我们的近似逆与预处理共轭梯度法的使用，并与该领域最近提出的一些也采用近似逆的算法进行了比较。在顺序和并行硬件假设下对所考虑的方法进行了比较。
A couple of approximate inversion techniques are presented which provide a parallel enhancement to several iterative methods for solving linear systems arising from the discretization of boundary value problems. In particular, the Jacobi, Gauss‐Seidel, and successive overrelaxation methods can be improved substantially in a parallel environment by the extensions considered. A special case convergence proof is presented. The use of our approximate inverses with the preconditioned conjugate gradient method is examined and comparisons are made with some recently proposed algorithms in this area that also employ approximate inverses. The methods considered are compared under sequential and parallel hardware assumptions.