Implicitly Restarted Arnoldi Methods and Subspace Iteration
Implicitly Restarted Arnoldi Methods and Subspace Iteration
复制标题
DOI：
10.1137/s0895479899358595
复制
发表时间：
2001-02
期刊：
影响因子：
--
通讯作者：
R. Lehoucq
中科院分区：
文献类型：
--
作者：
R. Lehoucq
本文的目的是提出一个优雅的隐式重新启动Arnoldi方法（IRAM）和非平稳（子空间）同时迭代之间的关系。这种关系允许由于Watkins和Elsner [Linear Algebra Appl.，143（1991），pp. 19- 47]，用于分析IRAM的收敛速率。我们还评论了与其他重新启动计划的关系。一组实验表明，隐式重新开始方法可以收敛速度比同时迭代时，迭代的子空间的相同的维数。
This goal of this paper is to present an elegant relationship between an implicitly restarted Arnoldi method (IRAM) and nonstationary (subspace) simultaneous iteration. This relationship allows the geometric convergence theory developed for nonstationary simultaneous iteration due to Watkins and Elsner [Linear Algebra Appl., 143 (1991), pp. 19--47] to be used for analyzing the rate of convergence of an IRAM. We also comment on the relationship with other restarting schemes. A set of experiments demonstrates that implicit restarted methods can converge at a much faster rate than simultaneous iteration when iterating on a subspace of equal dimension.