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本文提出一种可实现非线性方程最优拟合的新方法——缩张算法(Contraction-Expansion Algorithm,简称C-E算法)。该算法由若干循环组成,每一循环都包含收缩和扩张两个步骤。因而,可以在多维起始空间的内、外漫游搜索目标函数,并利用搜索过程所反馈的信息调整搜索中心和步长;通过较少次C-E循环的搜索,便能逼近给定非线性方程的最适参数值。该算法不需要给出方程的导数或偏导数,减少了计算的复杂性,也可能推广应用于解决其它目标函数的最优化问题。
In this paper, we propose a new method called Contraction-Expansion Algorithm (C-E), which can achieve the best fitting of nonlinear equations. The algorithm consists of several cycles, each cycle contains two steps of contraction and expansion. Therefore, the target function can be roamed inside and outside the multi-dimensional starting space, and the search center and step size can be adjusted by using the information fed back by the searching process. By searching less CE cycles, we can approach the given nonlinear equations The most suitable parameter value. The algorithm does not need to give the derivative or partial derivative of the equation, reduces the computational complexity, and may also be widely applied to solve the optimization problem of other objective functions.