IDR Explained
IDR Explained
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DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
M. Gutknecht
中科院分区：
文献类型：
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作者：
M. Gutknecht
诱导降维（Induced Dimension Reduction，IDR）方法是一种求解线性方程组的Krylov空间方法，由Peter Sonneveld在1979年左右提出。它并不是只有少数人使用，主要是作为Bi-CGSTAB的前身，后者是在10年后才推出的。在2007年，Sonneveld和货车Gijzen重新考虑了IDR，并将其推广到IDR（s），声称IDR（1）与IDR同样快，但优于密切相关的Bi-CGSTAB，并且s> 1的IDR（s）可能比Bi-CGSTAB快得多。当n s> 1时，IDR（s）与Yeung和Chan的ML（s）BiCGSTAB相关，IDR方法具有一定的灵活性。这种方法完全不同于传统的Krylov空间方法，因此需要额外的努力来熟悉它，并了解与更知名的Krylov空间方法的联系和差异。这篇简要的论文旨在提供一些帮助，并使该方法即使是非专家也能理解。在介绍了IDR及其相关方法的发展历史之后，我们总结了Krylov空间方法的一些基本事实。然后，我们详细介绍了原始IDR（s），并将其与其他方法相结合。具体分析了1980年发表的IDR方法、IDR（1）方法和Bi-CGSTAB方法之间的差异。在文章的最后，我们讨论了最近提出的一个巧妙的变种IDR（s）的残差满足额外的正交条件。在这里，我们详述了货车Gijzen和Sonneveld的出版物中遗漏的细节。
The Induced Dimension Reduction (IDR) method is a Krylov spa ce method for solving linear systems that was developed by Peter Sonneveld around 1979. It was not iced by only a few people, and mainly as the forerunner of Bi-CGSTAB, which was introduced a decade late r. In 2007, Sonneveld and van Gijzen reconsidered IDR and generalized it to IDR (s), claiming that IDR(1) ≈ IDR is equally fast but preferable to the closely related Bi-CGSTAB, and that IDR(s) with s > 1 may be much faster than Bi-CGSTAB. It also turned out that whe n s > 1, IDR(s) is related to ML(s)BiCGSTAB of Yeung and Chan, and that there is quite some flexib ility in the IDR approach. This approach differs completely from tradition al approaches to Krylov space methods, and therefore it requires an extra effort to get familiar with it and to unde rstand the connections as well as the differences to better-known Krylov space methods. This expository paper a ims to provide some help in this and to make the method understandable even to non-experts. After presenti ng the history of IDR and related methods, we summarize some of the basic facts on Krylov space methods. Then we prese nt th original IDR(s) in detail and put it into perspective with other methods. Specifically, we analyze th e differences between the IDR method published in 1980, IDR(1), and Bi-CGSTAB. At the end of the paper, we discuss a recently proposed ingenious variant of IDR(s) whose residuals fulfill extra orthogonality conditions. Th ere we dwell on details that have been left out in the publications of van Gijzen and Sonneveld.
DOI：
10.1137/0913035
发表时间：
1992-03-01
期刊：
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING
影响因子：
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作者：
VANDERVORST, HA
通讯作者：
VANDERVORST, HA
DOI：
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发表时间：
1984
期刊：
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影响因子：
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作者：
M. Wodzicki
通讯作者：
M. Wodzicki