{"title":"Greedy Randomized Kaczmarz with momentum method for nonlinear equation","authors":"Li Liu, Wei-Guo Li, Li-Li Xing, Wen-Di Bao","doi":"10.1016/j.cam.2024.116359","DOIUrl":null,"url":null,"abstract":"<div><div>Based on the nonlinear greedy randomized Kaczmarz (NGRK) method and the heavy ball method, a nonlinear greedy randomized Kaczmarz with momentum (NGRKm) method is presented for solving large nonlinear systems. Furthermore, the convergence of the NGRKm method is proved and the corresponding numerical experiments show the effectiveness of the NGRKm method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116359"},"PeriodicalIF":2.1000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724006071","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Based on the nonlinear greedy randomized Kaczmarz (NGRK) method and the heavy ball method, a nonlinear greedy randomized Kaczmarz with momentum (NGRKm) method is presented for solving large nonlinear systems. Furthermore, the convergence of the NGRKm method is proved and the corresponding numerical experiments show the effectiveness of the NGRKm method.
期刊介绍:
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.