Network flows that solve least squares for linear equations

作     者：Liu, Yang Lou, Youcheng Anderson, Brian D. O. Shi, Guodong 

作者机构：Australian Natl Univ Res Sch Elect Energy & Mat Engn Canberra ACT 0200 Australia Chinese Acad Sci Acad Math & Syst Sci MDIS Beijing 100190 Peoples R China Hangzhou Dianzi Univ Hangzhou 310018 Peoples R China Data61 CSIRO Canberra ACT 0200 Australia Univ Sydney Australian Ctr Field Robot Sydney NSW 2006 Australia 

出 版 物：《AUTOMATICA》 (自动学)

年 卷 期：2020年第120卷

页      面：109108-109108页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：Australian Research Council (ARC) [DP-130103610  DP-160104500  DP190103615] 

主　　题：Distributed algorithms Linear equation Least-squares solutions 

摘      要：This paper presents a first-order distributed continuous-time algorithm for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size, convergence results are provided for fixed graphs. The exact rate of convergence is also established for various types of step size choices falling into that category. For the case where non-unique solutions exist, convergence to one such solution is proved for constantly connected switching graphs with square integrable step size. Validation of the results and illustration of the impact of step size on the convergence speed are made using a few numerical examples. (C) 2020 Elsevier Ltd. All rights reserved.