A flexible block classical Gram–Schmidt skeleton with reorthogonalization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-19 DOI:10.1002/nla.2491

Qinmeng Zou

引用次数: 0

Abstract

We investigate a variant of the reorthogonalized block classical Gram–Schmidt method for computing the QR factorization of a full column rank matrix. Our aim is to bound the loss of orthogonality even when the first local QR algorithm is only conditionally stable. In particular, this allows the use of modified Gram–Schmidt instead of Householder transformations as the first local QR algorithm. Numerical experiments confirm the stable behavior of the new variant. We also examine the use of non‐QR local factorization and show by example that the resulting variants, although less stable, may also be applied to ill‐conditioned problems.

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具有重正交化的柔性块经典Gram-Schmidt骨架

我们研究了重新正交块经典Gram–Schmidt方法的一个变体，用于计算全列秩矩阵的QR因子分解。我们的目标是限制正交性的损失，即使当第一个局部QR算法仅条件稳定时也是如此。特别是，这允许使用修改的Gram–Schmidt而不是Householder变换作为第一个局部QR算法。数值实验证实了新变体的稳定行为。我们还研究了非QR局部因子分解的使用，并通过例子表明，所产生的变体虽然不太稳定，但也可以应用于病态问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.