解非线性方程的“区间一点迭代法”

Interval—Point Interactive Method for Solving Nonlinear Equations

对于求解非线性方程f(x)=0 (1)已形成许多方法。本文只叙述如何用区间一点迭代法求(1)的实根(后文所及也均指实根),至于求虚根将另文叙述。

This paper combines usual point interatave method with interval interactive method and forms the Interval__Point intercative method. The method neednt give the nonlinear funcrion f(x) any restraction, except continuation. The method, which neednt structure complicated interactive formulas, can extract a root of the nonlinear eguation f(x)=0 for the arbitrary finite interval [a, b] and the arbitrary initial value x. or conclude It hasnt any root. The method both voids more inconvenient interval computation, and can give the error estimation of the approximate solution. Its convergence is obvious. The rate of converence is usually identical with the corresponding point method, and its computational quantity, if are used compiled tacles of formulas, can decrease.