弦截法在非线性方程组的推广

The improvement of secant method in nonlinear equations

通过对求解非线性方程组的牛顿方法的研究,在介绍了求解非线性方程的弦截法和快速弦截法的基础上,给出了求解非线性方程组的弦截法。非线性方程组的弦截法实际上是弦截法从非线性方程的一个推广,该推广避免了牛顿方法在求解非线性方程组的过程中出现导数为0,或很小时带来的困难。还给出了弦截法求解非线性方程组的详细步骤,并结合具体算例验证了该方法的收敛性以及收敛速度。

algorithm nonlinear nonlinear Through solving nonlinear equations of the Newton method, based on the existing for solving equations secant method and fast secant method, the secant method of the equations is introduced. The secant method of the nonlinear equations is extension of equation. It avoids solving the derivative. The approach of the new secant method of nonlinear equations is detailed given, and the convergence and speed are proved through several examples.