摘要
提出一种求解非线性方程组的一元化方法，该方法可以将ｍ 元非线性方程组转化为与之有相同解的ｍ 个一元方程，从而使难以求解的非线性方程组变成很容易求解的一元方程。该方法收敛速度快，计算精度高，且不易发散。经过大量计算表明，许多用拟牛顿迭代法、梯度法、下降法等传统方法难以求解且易发散或收敛速度很慢的非线性方程组，采用本文方法都可以容易地求得它们的解。在此基础上还提出了多元二分法，它作为一元化方法的一个特例，非常适用于求解极值问题中遇到的非线性方程组。
A univariate method for solving nonlinear simultaneous equations is given in this paper. It can transform nonlinear simultaneous equations into univariate equations which solution is equivalent to that of the nonlinear simultaneous equations. The method has the advantages of high convergence rate, high computational accuracy, and furthermore, the global convergence that the result can be rapidly obtained with any initial point. Large amount of calculating examples have shown that many nonlinear simultaneous equations can be conveniently solved by the univariate method, while the traditional methods such as quasi Newton method, descent method and so on cannot solve those because of diverging easily and low convergence rate. As a special case of the univariate method, a multivariate dichotomy is also presented, which can be conveniently used to solve the nonlinear simultaneous equations encountered in extremum problems.
出处
《机械强度》
EI
CAS
CSCD
北大核心
1999年第3期205-207,共3页
Journal of Mechanical Strength
关键词
数值分析
非线性方程组
最优化
迭代法
numerical analysis,nonlinear equations,optimization,iteration method
