一类非线性方程组的求解

A Method to Solve a Class of Nonlinear Equation Systems

对于一个给定的非线性方程组,通过一系列的变化,可以将其构造成一个函数,从而把非线性方程组的求解问题转换为求函数极小值问题.通过利用正交表的数据分析方法,给出了求函数极小值进而求解非线性方程组的方法,这种方法得到的解比已有的更精确,且大大缩减了复杂方程组的计算量,用时少,不需要初始值.最后,采用Matlab软件,验证了其可行性和有效性.

For a given nonlinear equation systems, we can construct a function through a series of change. Then the problem to solve nonlinear equation systems is transformed to that to find function minimum. By the data analysis method of orthogonal design, this paper presents a general method to find function minimum and to solve the nonlinear equation systems. By this kind of method we can obtain more accurate solutions than the existing methods in [1-4]. And this method without the initial values greatly reduces the calculation of complex equation systems. Finally through simulation with Matlab language, the feasibility and effectiveness of this method are verified.