On interpolation variants of Newton's method for functions of several variables

被引：20

作者：

Cordero, A. ^{[1
]}

Torregrosa, Juan R. ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Valencia 46022, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 01期

关键词：

Nonlinear systems; Newton's method; Fixed point iteration; Convergence order;

D O I：

10.1016/j.cam.2009.12.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A generalization of the variants of Newton's method based on interpolation rules of quadrature is obtained, in order to solve systems of nonlinear equations. Under certain conditions, convergence order is proved to be 2d + 1, where d is the order of the partial derivatives needed to be zero in the solution. Moreover, different numerical tests confirm the theoretical results and allow us to compare these variants with Newton's classical method, whose convergence order is d + 1 under the same conditions. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：34 / 43

页数：10

共 14 条

[1] A modified Chebyshev's iterative method with at least sixth order of convergence [J].

Amat, S. ;

Hernandez, M. A. ;

Romero, N. .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 206 (01) :164-174

[2] NONLINEAR FEEDBACK-CONTROL FOR OPERATING A NONISOTHERMAL CSTR NEAR AN UNSTABLE STEADY-STATE [J].

BRUNS, DD ;

BAILEY, JE .

CHEMICAL ENGINEERING SCIENCE, 1977, 32 (03) :257-264

[3] Variants of Newton's Method using fifth-order quadrature formulas [J].

Cordero, A. ;

Torregrosa, Juan R. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (01) :686-698

[4] An optimization of Chebyshev's method [J].

Ezquerro, J. A. ;

Hernandez, M. A. .

JOURNAL OF COMPLEXITY, 2009, 25 (04) :343-361

[5]

EZQUERRO JA, 1999, REV ANAL NUMER THEOR, V28, P23

[6] Accelerated convergence in Newton's method [J].

Ford, WF ;

Pennline, JA .

SIAM REVIEW, 1996, 38 (04) :658-659

[7] Third-order methods from quadrature formulae for solving systems of nonlinear equations [J].

Frontini, A ;

Sormani, E .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 149 (03) :771-782

[8] Some variant of Newton's method with third-order convergence [J].

Frontini, M ;

Sormani, E .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 140 (2-3) :419-426

[9] A variant of Cauchy's method with accelerated fifth-order convergence [J].

Grau, M ;

Noguera, M .

APPLIED MATHEMATICS LETTERS, 2004, 17 (05) :509-517

[10]

Ortega J, 1970, Iterative solution of nonlinear equations in several variables

← 1 2 →