Noise propagation in linear stationary iterations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-23 DOI:10.1007/s11075-024-01890-0

Tommy Elfving

引用次数: 0

Abstract

We consider a stationary iteration for solving a linear system of arbitrary order. The method includes, e.g. Kaczmarz iteration, the Landweber iteration and the SOR (Gauss-Seidel) iteration. A study of the behavior of the iterates, both theoretically and experimentally, is performed. In particular we compare the behavior with and without noise in the data. The results give insight into the interplay between noise free and noisy iterates. For comparision we also included a Krylov type method CGLS in the experiments. As expected CGLS works well for noise free data but also tends to amplify the noise faster than the other methods, thus making it more critical when to stop the iterations.

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线性静态迭代中的噪声传播

我们考虑的是求解任意阶线性系统的静态迭代法。该方法包括 Kaczmarz 迭代、Landweber 迭代和 SOR（高斯-赛德尔）迭代等。我们从理论和实验两方面对迭代的行为进行了研究。特别是，我们比较了数据中有噪声和无噪声时的行为。结果让我们深入了解了无噪声迭代和有噪声迭代之间的相互作用。为了进行比较，我们还在实验中加入了克雷洛夫类型方法 CGLS。不出所料，CGLS 在无噪声数据中运行良好，但也比其他方法更快地放大噪声，因此何时停止迭代变得更为重要。

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.