求解欠定非线性方程组的两种无导数方法

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2011-01-01 DOI:10.1590/S1807-03022011000100011

N. Echebest, M. L. Schuverdt, R. Vignau

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引用次数: 5

摘要

本文提出了求解欠定非线性方程组的两种不同方法。在其中一种方法中，对La Cruz, Martinez和Raydan定义的求解平方非线性系统的无导数方法进行了修正和扩展，以处理欠定情况。另一种方法是准牛顿方法，它使用Broyden更新公式和全球化线搜索，将Grippo, Lampariello和Lucidi的策略与Li和Fukushima的策略结合起来。证明了两种方法的全局收敛性，并给出了数值实验。

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Two derivative-free methods for solving underdetermined nonlinear systems of equations

In this paper, two different approaches to solve underdetermined nonlinear system of equations are proposed. In one of them, the derivative-free method defined by La Cruz, Martinez and Raydan for solving square nonlinear systems is modified and extended to cope with the underdetermined case. The other approach is a Quasi-Newton method that uses the Broyden update formula and the globalized line search that combines the strategy of Grippo, Lampariello and Lucidi with the Li and Fukushima one. Global convergence results for both methods are proved and numerical experiments are presented.

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来源期刊

Computational & Applied Mathematics Mathematics-Computational Mathematics

CiteScore

4.50

自引率

11.50%

发文量

352

审稿时长

>12 weeks

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.