Faster Deterministic Pseudoinverse-Free Block Extension of Motzkin Method for Large Consistent Linear Systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-01 DOI:10.4208/eajam.2022-203.140123

J. Zhang

引用次数: 0

Abstract

. Recently, a fast deterministic block Kaczmarz (FDBK) method which uses a greedy criterion of the row selections and contains pseudoinverse-free computation is presented. In this work, we introduce a maximum residual rule into FDBK and develop a new block Kaczmarz method which is also considered as a fast deterministic pseudoinverse-free block extension of Motzkin (FBEM) method. In addition, we prove that FBEM converges linearly to the unique least-norm solution of the linear systems. Furthermore, by incorporating the Polyak momentum technique into the FBEM iteration method, we establish an accelerated variant of FBEM (mFBEM) and show its global linear convergence. Numerical examples using artiﬁcial and real datasets demonstrate the effectiveness of FBEM as well as mFBEM.

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大型一致线性系统的Motzkin方法的快速确定性伪逆块扩展

最近，提出了一种快速确定块Kaczmarz（FDBK）方法，该方法使用行选择的贪婪准则并包含伪逆自由计算。在这项工作中，我们在FDBK中引入了一个最大残差规则，并发展了一种新的块Kaczmarz方法，该方法也被认为是Motzkin（FBEM）方法的快速确定伪逆自由块扩展。此外，我们还证明了FBEM线性收敛于线性系统的唯一最小范数解。此外，通过将Polyak动量技术引入FBEM迭代方法，我们建立了FBEM的加速变体（mFBEM），并展示了其全局线性收敛性。使用人工和真实数据集的数值例子证明了FBEM和mFBEM的有效性。

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.