﻿ 一个求解非线性方程组问题的LS算法 A LS Algorithm for Nonlinear Equations

Vol.05 No.04(2016), Article ID:19126,5 pages
10.12677/AAM.2016.54093

A LS Algorithm for Nonlinear Equations

Linghua Huang

School of Information and Statistics, Guangxi University of Finance and Economics, Nanning Guangxi

Received: Nov. 12th, 2016; accepted: Nov. 26th, 2016; published: Nov. 30th, 2016

ABSTRACT

This paper presents a LS conjugate gradient algorithm for nonlinear equations and the given algorithm has the following features: 1) the search direction satisfies the sufficient descent property; 2) the direction also has the trust region property; 3) the proposed algorithm possesses the global convergence; 4) numerical results show that the new algorithm is effective.

1. 引言

(1.1)

(1.2)

(1.3)

2. 公式和算法

(2.1)

(2.2)

(2.3)

3. 下降性、信赖域性质和收敛性分析

(3.1)

(3.2)

(3.1)式成立。下证(3.2)式。根据(3.1)式，可推出

(B)上满足下面的Lipschitz性质，即

4. 数值结果

Table 1. Equations problem

A LS Algorithm for Nonlinear Equations[J]. 应用数学进展, 2016, 05(04): 813-817. http://dx.doi.org/10.12677/AAM.2016.54093

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