A semilocal convergence result for Newton's method under generalized conditions of Kantorovich

J.A. Ezquerro; D. Gonzalez; M.A. Hernandez-Veron

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A semilocal convergence result for Newton's method under generalized conditions of Kantorovich

机译：广义Kantorovich条件下牛顿法的半局部收敛结果。

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摘要

From Kantorovich's theory we establish a general semilocal convergence result for Newton's method based fundamentally on a generalization required to the second derivative of the operator involved. As a consequence, we obtain a modification of the domain of starting points for Newton's method and improve the a priori error estimates. Finally, we illustrate our study with an application to a special case of conservative problems.

机译：根据坎托罗维奇的理论，我们从根本上基于对所涉及算子的二阶导数的泛化，为牛顿法建立了一个一般的半局部收敛结果。结果，我们获得了牛顿法的起点域的修改，并改进了先验误差估计。最后，我们以保守问题的特殊情况为例说明了我们的研究。

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来源
《Journal of complexity》 |2014年第3期|309-324|共16页
作者
J.A. Ezquerro; D. Gonzalez; M.A. Hernandez-Veron;
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作者单位

University of La Rioja, Department of Mathematics and Computation, C/Luis de Ulloa s, 26004 Logrono, Spain;

University of La Rioja, Department of Mathematics and Computation, C/Luis de Ulloa s, 26004 Logrono, Spain;

University of La Rioja, Department of Mathematics and Computation, C/Luis de Ulloa s, 26004 Logrono, Spain;

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正文语种 eng
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关键词
Newton's method; Semilocal convergence; The Newton-Kantorovich theorem; Majorizing sequence; A priori error estimates; Conservative problem;

机译：牛顿法;半局部收敛;牛顿-坎托罗维奇定理;主序列;先验误差估计;保守问题;

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1. On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions [J] . Gutiérrez J.M., Magre?án á.A., Romero N. Applied mathematics and computation . 2013,第Null期

机译：中心-Lipschitz条件下Newton-Kantorovich方法的半局部收敛
2. A GENERAL SEMILOCAL CONVERGENCE RESULT FOR NEWTON'S METHOD UNDER CENTERED CONDITIONS FOR THE SECOND DERIVATIVE [J] . José Antonio Ezquerro, Daniel González, Miguel ángel Hernández ESAIM. Mathematical modelling and numerical analysis . 2013,第1期

机译：在二阶导数为中心条件下牛顿法的一般半收敛结果
3. Kantorovich-type semilocal convergence analysis for inexact Newton methods [J] . Argyros, I.K., Ren, H. Journal of Computational and Applied Mathematics . 2011,第9期

机译：不精确牛顿法的Kantorovich型半局部收敛性分析
4. A semilocal convergence theorem for Newton-type method under γ-condition in Banach space [C] . Minhong Chen, Wu Qingbiao 2011 International Conference on Multimedia Technology . 2011

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5. On the convergence and superconvergence of the Generalized Finite Element Methods [D] . Anitescu, Cosmin. 2010

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6. Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions [O] . Yueqing Zhao, Rongfei Lin, Zdenek Šmarda, 2015

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7. Kantorovich-type semilocal convergence analysis for inexact Newton methods [O] . Argyros Ioannis K., Ren Hongmin 2011

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A semilocal convergence result for Newton's method under generalized conditions of Kantorovich

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