求方程全部实根的一个二阶方法

本文建立了一个求解单变元非线性方程f(x)=0全部实根的一个二阶方法:(n=0,1,2,……) 且当根号前取“+”号时所得的序列{X_n}单调增地收于X_o右侧距X_o最近的实根;当根号前取“-”号时所得到的序列{X_n}单调递减地收敛于X_o左侧距X_o最近的实根。该方法初值选取任意,敛速与牛顿法相当,是非线性方程求解行之有的方法之一.

A TWO ORDER METHOD FOR FINDING ALL REAL ROOTS OF NONLIAEARE EQUATIONS

In this paper a two order method has been established of finding all real roots of nonlinear equations including one variable. and taking sign " + " in front of the radical, we obtain sequences { xo } which monotone increasing converges to a real root at x_0 right side and distance from it to x_0 is nearest; if taking sign "-", we obtain sequences{ x_n } which monotone decreasing converges to a real root at left side and distance from it to x_0 is nearest The choice of the method's initial value is any and the convergence rate is equivalent to Newton's method Therefore it is one of the effecfual measures in practice