A DIMENSION-REDUCING METHOD FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS IN RN

被引：9

作者：

GRAPSA, TN ^{[1
]}

VRAHATIS, MN ^{[1
]}

机构：

[1] CORNELL UNIV,DEPT MATH,ITHACA,NY 14853

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 1990年 / 32卷 / 3-4期

关键词：

bisection method; Implicit function theorem; imprecise function values; m-step SOR-Newton; Newton's method; nonlinear SOR; numerical solution; quadratic convergence; reduction to one-dimensional equations; systems of nonlinear equations; zeros;

D O I：

10.1080/00207169008803828

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A method for the numerical solution of systems of nonlinear algebraic and/or transcendental equations in [formula omitted] is presented. This method reduces the dimensionality of the system in such a way that it can lead to an iterative approximate formula for the computation of n— 1 components of the solution. while the remaining component of the solution is evaluated separately using the final approximations of the other components. This (n 11-dimensional iterative formula generates a sequence of points in [formula omitted] which converges quadratically to n-1 components of the solution. Moreover, it does not require a good initial guess for one component of the solution and it does not directly perform function evaluations, thus it can be applied to problems with imprecise function values. A proof of convergence is given and numerical applications are presented. © 1990, Taylor & Francis Group, LLC. All rights reserved.

引用

页码：205 / 216

页数：12