Greedy Block Extended Kaczmarz Method for Solving the Least Squares Problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-29 DOI:10.1007/s40840-024-01739-8

Ni-Hong Ke, Rui Li, Jun-Feng Yin

引用次数: 0

Abstract

A greedy block extended Kaczmarz method is introduced for solving the least squares problem where the greedy rule combines the maximum-distances with relaxation parameters. In order to save the computational cost of Moore–Penrose inverse, an average projection technique is used. The convergence theory of the greedy block extended Kaczmarz method is established and an upper bound for the convergence rate is also derived. Numerical experiments show that the proposed method is efficient and better than the randomized block extended Kaczmarz methods in terms of the number of iteration steps and computational time.

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解决最小二乘法问题的贪心块扩展卡茨马兹法

为解决最小二乘法问题引入了一种贪婪块扩展 Kaczmarz 方法，其中贪婪规则结合了最大距离和松弛参数。为了节省 Moore-Penrose 逆的计算成本，采用了平均投影技术。建立了贪心块扩展 Kaczmarz 方法的收敛理论，并推导出收敛率上限。数值实验表明，在迭代步数和计算时间方面，所提出的方法比随机块扩展 Kaczmarz 方法更有效、更优。

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.