解非线性方程的免导数牛顿算法

A Gradient-free Newton Method for Nonlinear Equation

通过函数值的运算近似牛顿法中的导数项,构造了一个免导数的牛顿法.该算法与牛顿法一样,具有二阶收敛速度,但不需要用到函数的导数.通过与二分法结合,实现该算法的全局收敛性.数值结果表明该算法是有效的.

This paper first proposed a gradient-free method for nonlinear equation by approximating the derivative term in the Newton method.Like the Newton method,the algorithm is convergent two-order.Moreover,a globally convergent derivative-free method was presented by combining the above gradient-free method with the bisection method.Some numerical results show that the algorithm is effective.