{"title":"求解非线性方程的七阶收敛牛顿型方法","authors":"Yunhong Hu, Liang Fang","doi":"10.1109/CINC.2010.5643798","DOIUrl":null,"url":null,"abstract":"In this paper, we present a seventh-order convergent Newton-type method for solving nonlinear equations which is free from second derivative. At each iteration it requires three evaluations of the given function and two evaluation of its first derivative. Therefore its efficiency index is equal to equation which is better than that of Newton's method √2. Several examples demonstrate that the algorithm is more efficient than classical Newton's method and other existing methods.","PeriodicalId":227004,"journal":{"name":"2010 Second International Conference on Computational Intelligence and Natural Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2010-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A seventh-order convergent Newton-type method for solving nonlinear equations\",\"authors\":\"Yunhong Hu, Liang Fang\",\"doi\":\"10.1109/CINC.2010.5643798\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a seventh-order convergent Newton-type method for solving nonlinear equations which is free from second derivative. At each iteration it requires three evaluations of the given function and two evaluation of its first derivative. Therefore its efficiency index is equal to equation which is better than that of Newton's method √2. Several examples demonstrate that the algorithm is more efficient than classical Newton's method and other existing methods.\",\"PeriodicalId\":227004,\"journal\":{\"name\":\"2010 Second International Conference on Computational Intelligence and Natural Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 Second International Conference on Computational Intelligence and Natural Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CINC.2010.5643798\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 Second International Conference on Computational Intelligence and Natural Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CINC.2010.5643798","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A seventh-order convergent Newton-type method for solving nonlinear equations
In this paper, we present a seventh-order convergent Newton-type method for solving nonlinear equations which is free from second derivative. At each iteration it requires three evaluations of the given function and two evaluation of its first derivative. Therefore its efficiency index is equal to equation which is better than that of Newton's method √2. Several examples demonstrate that the algorithm is more efficient than classical Newton's method and other existing methods.
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