{"title":"多多项式根牛顿法加速收敛方法的比较","authors":"J. McNamee","doi":"10.1145/290590.290592","DOIUrl":null,"url":null,"abstract":"Newton's method for solving polynomial equations converges only linearly to a multiple root. The speed of several methods for accelerating the convergence have been compared numerically. The Madsen-Reid method proved to be the fastest, with the Aitken and Ostrowsky methods close behind.","PeriodicalId":177516,"journal":{"name":"ACM Signum Newsletter","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"A comparison of methods for accelerating convergence of Newton's method for multiple polynomial roots\",\"authors\":\"J. McNamee\",\"doi\":\"10.1145/290590.290592\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Newton's method for solving polynomial equations converges only linearly to a multiple root. The speed of several methods for accelerating the convergence have been compared numerically. The Madsen-Reid method proved to be the fastest, with the Aitken and Ostrowsky methods close behind.\",\"PeriodicalId\":177516,\"journal\":{\"name\":\"ACM Signum Newsletter\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Signum Newsletter\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/290590.290592\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Signum Newsletter","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/290590.290592","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A comparison of methods for accelerating convergence of Newton's method for multiple polynomial roots
Newton's method for solving polynomial equations converges only linearly to a multiple root. The speed of several methods for accelerating the convergence have been compared numerically. The Madsen-Reid method proved to be the fastest, with the Aitken and Ostrowsky methods close behind.
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