解超越方程的平行弦方法

众所周知,牛顿法和弦截法是解超越方程的两个最简单和常用的方法.其中弦截法无需计算导数,实用上较方便,但牛顿法有更快的敛速.另一常用的抛物线法,虽然在敛速方面比弦截法有所提高,但它的每一步迭代却较复杂,而且敛速阶数低于牛顿法.所以,就计算效能而言,这三个方法各有优缺点.

A PARALLEL SECANT METHOD FOR SOLVING TRANSCENDENTAL EQUATION

In order to solve approximately the transcendental equation: f(x)= 0,an iteration method is presented with the following formula: y_(n+1)= x_n-f(x_n)/f(x_n,x_(n-1)), x_(n+1)= y_(n+1)-f(y_(n+1))/f(x_n,x_(n-1)),where f(x_n,x_(n-1))=f(x_n)-f(x_(n-1))]/x_n-x_(n-1)]. This method, which is called parallel secant method, provides the second order con-vergent speed as that of Newton-Raphson method and is better than the Muller methodused for iterations.