陈海霞. 基于凝聚函数法的非线性方程组求解[J]. 科学技术与工程, 2010, (6): .
chenhaixia.Solving Nonlinear Equations Problem Based on Aggregate Function Method[J].Science Technology and Engineering,2010,(6):. |
| 基于凝聚函数法的非线性方程组求解 |
| Solving Nonlinear Equations Problem Based on Aggregate Function Method |
| 投稿时间：2009-11-17 修订日期：2009-11-17 |
| DOI： |
| 中文关键词: 非线性方程组 凝聚函数 不可微优化 无约束优化 |
| 英文关键词:Nonlinear equations aggregate function non-differentiable optimization unconstrained optimization. |
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| 摘要点击次数: 1698 |
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| 中文摘要: |
| 本文给出了求解非线性方程组问题的一种有效方法，称为凝聚函数法。首先把非线性方程组转化为一个不可微优化问题，然后用一个称之为凝聚函数的光滑函数直接代替不可微的极大值函数，从而可把非线性方程组的求解转化为无约束优化问题，因此可以直接利用现有的无约束优化算法软件求解。在此基础了，我们给出了相应算法，并做了数值实验，数值实验结果表明了该算法具有收敛稳定，算法简单及计算效率高等优点。 |
| 英文摘要: |
| This paper presents a very efficient method, referred to as the aggregate function method, for solving nonlinear equations. First, nonlinear equations problem was be transformed to non-differentiable optimization, Then using the smooth aggregate function to instead of maximum function in non-differentiable optimization problem, Thereupon, the primal problem can be transformed into unconstrained optimization, so we can apply the algorithm or software of unconstrained optimization to solve the problems. On this basis, we give the method to solve nonlinear equations, and numerical experiment results demonstrate that the proposed method has advantages of stable convergence, easy implementation and high efficiency. |
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