{"title":"牛顿方法中kantorovich型定理的扩展","authors":"I. Argyros, S. George, D. R. Sahu","doi":"10.4064/am2352-1-2018","DOIUrl":null,"url":null,"abstract":". We extend the applicability of Newton’s method, so we can approximate a locally unique solution of a nonlinear equation in a Banach space setting in cases not covered before. To achieve this, we find a more precise set containing the Newton iterates than in earlier works.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"51 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extensions of Kantorovich-type theorems for Newton’s method\",\"authors\":\"I. Argyros, S. George, D. R. Sahu\",\"doi\":\"10.4064/am2352-1-2018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We extend the applicability of Newton’s method, so we can approximate a locally unique solution of a nonlinear equation in a Banach space setting in cases not covered before. To achieve this, we find a more precise set containing the Newton iterates than in earlier works.\",\"PeriodicalId\":52313,\"journal\":{\"name\":\"Applicationes Mathematicae\",\"volume\":\"51 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicationes Mathematicae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4064/am2352-1-2018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicationes Mathematicae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/am2352-1-2018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Extensions of Kantorovich-type theorems for Newton’s method
. We extend the applicability of Newton’s method, so we can approximate a locally unique solution of a nonlinear equation in a Banach space setting in cases not covered before. To achieve this, we find a more precise set containing the Newton iterates than in earlier works.
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