A GENERALIZED NEWTON-RAPHSON METHOD USING CURVATURE

被引：3

作者：

LEE, IW ^{[1
]}

JUNG, GH ^{[1
]}

机构：

[1] KOREA ADV INST SCI & TECHNOL,DEPT MECH ENGN,TAEJON 305701,SOUTH KOREA

来源：

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING | 1995年 / 11卷 / 09期

关键词：

NEWTON-RAPHSON METHOD; CURVATURE; LINE SEARCH ALGORITHM; NONLINEAR PROBLEM;

D O I：

10.1002/cnm.1640110906

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

A numerical method for finding the roots of any function is developed. This method considers a circle using the concept of curvature instead of the tangential line in the Newton-Raphson method. The compared results between the proposed method and the Newton-Raphson method are listed. The proposed method has a wider convergent region of initial points and finds more proper solutions than the Newton-Raphson method. In particular, the paper proposes that the curvature method is replaced by the modified Newton method discussed by Ralston in dealing with multiple roots.

引用

页码：757 / 763

页数：7

共 11 条

[1]

Zienkiewicz O.C., The Finite Element Method, (1977)

[2]

Arora J.S., Introduction to Optimum Design, (1989)

[3]

Hornbeck, Numerical Methods, (1975)

[4]

Carnahan, Luther H.A., Wilkes, Applied Numerical Methods, (1969)

[5]

Pearson, Handbook of Applied Mathematics, (1974)

[6]

de Araujo J.M., Optimization of Newton–Raphson methods in RC nonlinear analysis, Comput. Struct., 33, 3, (1989)

[7]

Bathe K.J., Finite Element Procedures in Engineering Analysis, (1982)

[8]

Nayak G.C., Zienkiewicz O.C., Note on the “alpha” ‐constant stiffness method for the analysis of non‐linear problems, Int. J. Numer. Methods Eng., 4, (1972)

[9]

Jennings A., Accelerating the convergence of matrix iterative processes, IMA Journal of Applied Mathematics, 8, (1971)

[10]

Aitken A.C., On the iterative solution of a system of linear equations, Proc. R. Soc. Edin., 63, (1950)

← 1 2 →