Local convergence of a relaxed two-step Newton like method with applications
 作者： I. K. Argyros,  Á. A. Magreñán,  L. Orcos,  J. A. Sicilia 作者单位： 1Cameron University2Universidad Internacional de La Rioja (UNIR) 刊名： Journal of Mathematical Chemistry, 2017, Vol.55 (7), pp.1427-1442 来源数据库： Springer Nature Journal DOI： 10.1007/s10910-016-0722-8 关键词： Two-step Newton’s method;  Banach space;  Fréchet derivative;  Divided difference of first order;  Local–semilocal convergence;  65D10;  65D99; 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.

• 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