{"title":"One-Parameter Third-Order Iterative Methods for Solving Nonlinear Equations","authors":"J. An, Yuan Yuan","doi":"10.1109/ICIC.2011.88","DOIUrl":null,"url":null,"abstract":"In this paper, we present a modification of the two-step Newton's method which produces a class of one-parameter iterative methods for solving nonlinear equations. An interpolating polynomial is constructed to avoid the evaluation of derivative. The convergence analysis shows that the new methods are third-order convergent and require one function and two first derivative evaluations per iteration. Several numerical examples are given to illustrate the performance of the presented methods.","PeriodicalId":6397,"journal":{"name":"2011 Fourth International Conference on Information and Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2011-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 Fourth International Conference on Information and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICIC.2011.88","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we present a modification of the two-step Newton's method which produces a class of one-parameter iterative methods for solving nonlinear equations. An interpolating polynomial is constructed to avoid the evaluation of derivative. The convergence analysis shows that the new methods are third-order convergent and require one function and two first derivative evaluations per iteration. Several numerical examples are given to illustrate the performance of the presented methods.
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