{"title":"New Kantorovich-Type Conditions for Halley's Method","authors":"J. A. Ezquerro, M. A. Hernández","doi":"10.1002/anac.200410024","DOIUrl":null,"url":null,"abstract":"<p>Two new semilocal convergence results of Newton-Kantorovich type are presented for the Halley method, where the usual convergence conditions, which appears in the literature, are relaxed. In one of them, it is supposed that the second derivative <i>F</i>″ of a nonlinear operator <i>F</i> satisfies ‖<i>F</i>″(<i>x</i><sub>0</sub>)‖ ≤ <i>α</i> instead of ‖<i>F</i>″(<i>x</i>)‖ ≤ <i>M</i>, for all <i>x</i> in a subset of the domain of <i>F</i>, where <i>α</i> and <i>M</i> are positive real constants. In the other one fewer convergence conditions are required than all the existing ones until now. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)</p>","PeriodicalId":100108,"journal":{"name":"Applied Numerical Analysis & Computational Mathematics","volume":"2 1","pages":"70-77"},"PeriodicalIF":0.0000,"publicationDate":"2005-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/anac.200410024","citationCount":"33","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Analysis & Computational Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/anac.200410024","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 33
Abstract
Two new semilocal convergence results of Newton-Kantorovich type are presented for the Halley method, where the usual convergence conditions, which appears in the literature, are relaxed. In one of them, it is supposed that the second derivative F″ of a nonlinear operator F satisfies ‖F″(x0)‖ ≤ α instead of ‖F″(x)‖ ≤ M, for all x in a subset of the domain of F, where α and M are positive real constants. In the other one fewer convergence conditions are required than all the existing ones until now. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
哈雷方法的新kantorovich型条件
给出了Halley方法的两个新的Newton-Kantorovich型半局部收敛结果，放宽了文献中常见的收敛条件。其中，假设非线性算子F的二阶导数F″满足‖F″(x0)‖≤α而不是‖F″(x)‖≤M，对于F定义域子集中的所有x，其中α和M是正实常数。在另一种情况下，所需的收敛条件比目前所有的收敛条件都要少。(©2005 WILEY-VCH Verlag GmbH &KGaA公司，Weinheim)
本文章由计算机程序翻译，如有差异，请以英文原文为准。
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
