THIRD-ORDER DIRECTIONAL NEWTON METHOD FOR MULTIVARIABLE EQUATIONS

被引：0

作者：

Kou Ji-sheng ^{[1
]}

Wang Xiu-hua ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

DCABES 2009: THE 8TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING AND APPLICATIONS TO BUSINESS, ENGINEERING AND SCIENCE, PROCEEDINGS | 2009年

关键词：

Parallel numerical algorithm; Nonlinear equations; Directional Newton method; Iterative method;

D O I：

暂无

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present a variant of the directional Newton method for solving a single nonlinear equation in several variables. Under suitable assumptions, we prove the cubic convergence speed of this new method. This method is suitable for parallel implements. The related parallel algorithms are discussed. Numerical examples show that the new method is feasible and efficient, and has better numerical behavior than the directional Newton method.

引用

页码：70 / 72

页数：3

共 9 条

[1] Directional secant method for nonlinear equations [J].

An, HB ;

Bai, ZZ .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 175 (02) :291-304

[2] On Newton-type methods with cubic convergence [J].

Homeier, HHH .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 176 (02) :425-432

[3] Third-order modification of Newton's method [J].

Kou Jisheng ;

Li Yitian ;

Wang Xiuhua .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 205 (01) :1-5

[4]

Levin Y, 2002, MATH COMPUT, V71, P251, DOI 10.1090/S0025-5718-01-01332-1

[5]

LUKTACS G, 1989, THEORY PRACTICE GEOM, P167

[6]

Ortega JM., 1970, Iterative Solution of Nonlinear Equations in Several Variables

[7]

Polyak Boris, 1987, Introduction to Optimization

[8]

Potra F.A., 1984, Research Notes in Mathematics, V103

[9] A composite third order Newton-Steffensen method for solving nonlinear equations [J].

Sharma, JR .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 169 (01) :242-246

← 1 →