Inertial randomized Kaczmarz algorithms for solving coherent linear systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-05 DOI:10.1007/s11075-024-01872-2

Songnian He, Ziting Wang, Qiao-Li Dong

引用次数: 0

Abstract

In this paper, by regarding the two-subspace Kaczmarz method as an alternated inertial randomized Kaczmarz algorithm we present a better convergence rate estimate under a mild condition. Furthermore, we accelerate the alternated inertial randomized Kaczmarz algorithm and introduce a multi-step inertial randomized Kaczmarz algorithm which is proved to have a faster convergence rate. Numerical experiments support the theory results and illustrate that the multi-inertial randomized Kaczmarz algorithm significantly outperform the two-subspace Kaczmarz method in solving coherent linear systems.

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求解相干线性系统的惯性随机卡兹马兹算法

在本文中，我们将双子空间 Kaczmarz 方法视为交替惯性随机 Kaczmarz 算法，在温和条件下提出了更好的收敛率估计。此外，我们加速了交替惯性随机化 Kaczmarz 算法，并引入了一种多步惯性随机化 Kaczmarz 算法，该算法被证明具有更快的收敛速度。数值实验支持了理论结果，并说明多惯性随机 Kaczmarz 算法在求解相干线性系统时明显优于双子空间 Kaczmarz 方法。

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.