A GENERAL SEMILOCAL CONVERGENCE RESULT FOR NEWTON'S METHOD UNDER CENTERED CONDITIONS FOR THE SECOND DERIVATIVE

被引：5

作者：

Antonio Ezquerro, Jose ^{[1
]}

Gonzalez, Daniel ^{[1
]}

Angel Hernandez, Miguel ^{[1
]}

机构：

[1] Univ La Rioja, Dept Math & Computat, Logrono 26004, Spain

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2013年 / 47卷 / 01期

关键词：

Newton's method; the Newton-Kantorovich theorem; semilocal convergence; majorizing sequence; a priori error estimates; Hammerstein's integral equation; OPERATORS; THEOREM; EQUATIONS;

D O I：

10.1051/m2an/2012026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

From Kantorovich's theory we present a semilocal convergence result for Newton's method which is based mainly on a modification of the condition required to the second derivative of the operator involved. In particular, instead of requiring that the second derivative is bounded, we demand that it is centered. As a consequence, we obtain a modification of the starting points for Newton's method. We illustrate this study with applications to nonlinear integral equations of mixed Hammerstein type.

引用

页码：149 / 167

页数：19

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