Pivoting strategies for tough sparse indefinite systems
Pivoting strategies for tough sparse indefinite systems
复制标题
困难稀疏不定系统的旋转策略
DOI：
10.1145/2513109.2513113
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
J. Scott
中科院分区：
文献类型：
--
作者：
Jonathan D. Hogg;J. Scott
稀疏直接求解器的性能取决于在分解开始之前选择的枢轴序列。在对称的不确定系统的情况下，可能有必要在分解过程中修改该序列以确保数值稳定性。这些修改在时间上可能会产生严重的后果，以及分解和后续解决方案所需的记忆和失败。这项研究着重于难以解决的稀疏对称不确定问题，标准阈值部分枢纽会导致重大修改。我们对旨在减少修改而不影响数值稳定性的核心策略进行了详细的综述。对实际应用引起的一系列棘手问题进行了广泛的数值实验。根据我们的发现，我们提出有关使用哪种策略的建议，尤其是建议一种基于匹配的方法来用于数值挑战性问题。
The performance of a sparse direct solver is dependent upon the pivot sequence that is chosen before the factorization begins. In the case of symmetric indefinite systems, it may be necessary to modify this sequence during the factorization to ensure numerical stability. These modifications can have serious consequences in terms of time as well as the memory and flops required for the factorization and subsequent solves. This study focuses on hard-to-solve sparse symmetric indefinite problems for which standard threshold partial pivoting leads to significant modifications. We perform a detailed review of pivoting strategies that are aimed at reducing the modifications without compromising numerical stability. Extensive numerical experiments are performed on a set of tough problems arising from practical applications. Based on our findings, we make recommendations on which strategy to use and, in particular, a matching-based approach is recommended for numerically challenging problems.
DOI：
10.1145/1499096.1499098
发表时间：
2009-03
期刊：
ACM Trans. Math. Softw.
影响因子：
--
作者：
J. Reid;J. Scott
通讯作者：
J. Reid;J. Scott
用于求解稀疏对称线性系统的快速、鲁棒的混合精度求解器
影响因子：
2.7
作者：
Hogg J
通讯作者：
Hogg J