非线性方程大范围内多根求解的一种方法

A Method for Solving More Roots of Nonlinear Equation in Large Scope

在假设非线性方程f(x)=0在[a,b]内有多个单根的前提下,令F(x)=f2(x),应用凸函数的性质,使大范围区间[a,b]内的初值很快过渡到F(x)每个最小极值点的邻域内,即方程每个根的邻域内,然后采用求根迭代公式得f(x)=0在[a,b]内的每个根,并给出了相应的算法和算例进行验证.特别是作为特殊情形,在求方程的一个根时,该方法要比传统的方程求根法快得多.

Under the premise of the assumption that the nonlinear equation f(x)=0 has more simple roots in ,making F(x)=f2(x),and applying the properties of convex function,the initial value in the large scope passed through to the neighbor of the each minimum extreme point of F(x) that is also the neighbor of the each root of the equation.Then each root of the nonlinear equation f(x)=0 was obtained using the iterative formula.The relevant algorithm and numerical example were given to verify in the end.This method is much faster than the traditional methods especially when the equation has one root.