Local convergence of a relaxed two-step Newton like method with applications
作者: I. K. ArgyrosÁ. A. MagreñánL. OrcosJ. A. Sicilia
作者单位: 1Cameron University
2Universidad Internacional de La Rioja (UNIR)
刊名: Journal of Mathematical Chemistry, 2017, Vol.55 (7), pp.1427-1442
来源数据库: Springer Journal
DOI: 10.1007/s10910-016-0722-8
关键词: Two-step Newton’s methodBanach spaceFréchet derivativeDivided difference of first orderLocal–semilocal convergence65D1065D99
英文摘要: We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fréchet derivative and on the center divided-difference of order one are used. In earlier studies such as Amat et al. (Numer Linear Algebra Appl 17:639–653, 2010 , Appl Math Lett 25(12):2209–2217, 2012 , Appl Math Comput 219(24):11341–11347, 2013 , Appl Math Comput 219(15):7954–7963, 2013 , Reducing Chaos and bifurcations in Newton-type methods. Abstract and applied analysis. Hindawi Publishing Corporation, Cairo, 2013 ) these methods are analyzed under hypotheses up to the second Fréchet derivative and divided differences of order one. Numerical examples are also provided in this work.
原始语种摘要: We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fréchet derivative and on the center divided-difference of order one are used. In earlier studies such as Amat et al. (Numer Linear Algebra Appl 17:639–653, 2010 , Appl Math Lett 25(12):2209–2217, 2012 , Appl Math Comput 219(24):11341–11347, 2013 , Appl Math Comput 219(15):7954–7963, 2013 , Reducing Chaos and bifurcations in Newton-type methods. Abstract and applied analysis. Hindawi Publishing Corporation, Cairo, 2013 ) these methods are analyzed under hypotheses up to the second Fréchet derivative and divided differences of order one. Numerical examples are also provided in this work.
全文获取路径: Springer  (合作)
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影响因子:1.226 (2012)

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关键词翻译
关键词翻译
  • convergence 汇合
  • Newton 牛顿
  • derivative 衍生物
  • method 方法
  • divided 分部联箱
  • analysis 分析
  • approximate 近似的
  • first 第一
  • earlier 早期的
  • relaxed 放松