{"title":"高度过定线性系统的斜投影计数草图最大加权残差Kaczmarz方法","authors":"Peng Zhang, Longyan Li, Pingping Zhang","doi":"10.4236/apm.2022.124020","DOIUrl":null,"url":null,"abstract":"Motivated by the count sketch maximal weighted residual Kaczmarz (CSMWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Count Sketch Maximal Weighted Residual Kaczmarz Method with Oblique Projection for Highly Overdetermined Linear Systems\",\"authors\":\"Peng Zhang, Longyan Li, Pingping Zhang\",\"doi\":\"10.4236/apm.2022.124020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by the count sketch maximal weighted residual Kaczmarz (CSMWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods.\",\"PeriodicalId\":43512,\"journal\":{\"name\":\"Advances in Pure and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4236/apm.2022.124020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4236/apm.2022.124020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Count Sketch Maximal Weighted Residual Kaczmarz Method with Oblique Projection for Highly Overdetermined Linear Systems
Motivated by the count sketch maximal weighted residual Kaczmarz (CSMWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods.
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