A systematic search method for obtaining multiple solutions of simultaneous nonlinear equations

Author

Chao, Kwong-Shu ; Liu, Dan-kai ; Pan, Ching-tsai

Volume

Issue

fYear

1975

fDate

9/1/1975 12:00:00 AM

Firstpage

748

Lastpage

753

Abstract

A systematic search method has been developed for obtaining the multiple solutions of a nonlinear equation of the form $f(x) = 0$ , where f is a continuously differentiable function from $R^n \\rightarrow R^n$ . The method is based on numerical integration of the associated system of differential equations $\\dot{f}_i = -f_i$ for $i = 1, 2,\\cdots , n - 1$ and $\\dot{f}_n = \\pm f_n$ along the space curve $l$ of intersection $f_i(x) = 0, i = 1, 2,\\cdots , n - 1$ . The plus or minus sign is chosen so as to make ${x_k}$ move in the desired direction on $l$ .

Keywords

Nonlinear algebraic equations; Nonlinear networks and systems; Chaos; Differential equations; Helium; Iterative methods; Jacobian matrices; Newton method; Nonlinear equations; Nonlinear systems; Piecewise linear techniques; Search methods;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/TCS.1975.1084122

Filename

1084122

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1176687