具有双侧广义瑞利商位移的QZ算法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-11-10 DOI:10.1002/nla.2475

X. Chen, Hongguo Xu

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引用次数: 0

摘要

我们推广了最近提出的QR算法中使用的双侧瑞利商单频移和双侧Grassmann–Rayleigh商双频移，并将广义版本应用于QZ算法。对于这样的移位策略，QZ算法通常具有三次局部收敛速度。我们的主要关注点是修改后的转换策略及其相应的截断版本。数值算例证明了带有所提出的移位的QZ算法的收敛性和效率。对于截断的版本，不提供局部收敛性分析。数值算例表明，它们优于修正位移和标准瑞利商单位移和弗朗西斯双位移。

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QZ algorithm with two‐sided generalized Rayleigh quotient shifts

We generalize the recently proposed two‐sided Rayleigh quotient single‐shift and the two‐sided Grassmann–Rayleigh quotient double‐shift used in the QR algorithm and apply the generalized versions to the QZ algorithm. With such shift strategies the QZ algorithm normally has a cubic local convergence rate. Our main focus is on the modified shift strategies and their corresponding truncated versions. Numerical examples are provided to demonstrate the convergence properties and the efficiency of the QZ algorithm equipped with the proposed shifts. For the truncated versions, local convergence analysis is not provided. Numerical examples show they outperform the modified shifts and the standard Rayleigh quotient single‐shift and Francis double‐shift.

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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.