On the global convergence of Chebyshev's iterative method

被引：17

作者：

Amat, S. ^{[1
]}

Busquier, S. ^{[1
]}

Gutierrez, J. M. ^{[2
]}

Hernandez, M. A. ^{[2
]}

机构：

[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain

[2] Univ La Rioja, Dept Matemat & Computac, La Rioja, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2008年 / 220卷 / 1-2期

关键词：

nonlinear equations; iterative methods; geometry global convergence;

D O I：

10.1016/j.cam.2007.07.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In [A. Melman, Geometry and convergence of Euler's and Halley's methods, SIAM Rev. 39(4) (1997) 728-735] the geometry and global convergence of Euler's and Halley's methods was studied. Now we complete Melman's paper by considering other classical third-order method: Chebyshev's method. By using the geometric interpretation of this method a global convergence theorem is performed. A comparison of the different hypothesis of convergence is also presented. (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：17 / 21

页数：5

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