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

作　　者：陈海霞[1] 杨铁贵[1] 

机构地区：[1]郑州职业技术学院基础教育处,郑州450121

出　　处：《科学技术与工程》2010年第6期1494-1496,1505,共4页Science Technology and Engineering

摘　　要：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。在此基础上,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。A very efficient method is presented, referred to as the aggregate function method, for solving nonlinear equations. First, nonlinear equations problem is 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 the algorithm or software of unconstrained optimization can be applied to solve the problems. On this basis, the method to solve nonlinear equations is given, and numerical experiment results demonstrate that the proposed method has advantages of stable convergence, easy implementation and high efficiency.

关 键 词：非线性方程组 凝聚函数 不可微优化 无约束优化 

分 类 号：O241.7[理学—计算数学]