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单词 Secant search
释义

Secant search

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割线法 Secant method

(重定向自Secant search)
割线法的最初两个迭代。红色曲线表示函数f,蓝色曲线表示割线。

在数值分析中,割线法是一个求根算法,该方法用一系列割线的根来近似代替函数f的根。

割线法由以下的递推关系定义:

x_{n+1} = x_n - \frac{x_n-x_{n-1}}{f(x_n)-f(x_{n-1})} f(x_n).

从上式中可以看出,割线法需要两个初始值x0x1,它们离函数的根越近越好。

英语百科

Secant method 割线法

(重定向自Secant search)
The first two iterations of the secant method. The red curve shows the function f and the blue lines are the secants. For this particular case, the secant method will not converge.

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite difference approximation of Newton's method. However, the method was developed independently of Newton's method, and predates it by over 3,000 years.

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更新时间:2025/6/17 17:13:27