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词汇 Bisection method
分类 英语词汇 英语翻译词典
释义

Bisection method

中文百科

二分法 (数学)

A few steps of the bisection method applied over the starting range [a1;b1]. The bigger red dot is the root of the function.

二分法英语:Bisection method),是一种方程序根的近似值求法。

若要求已知函数 f(x) = 0 的根 (x 的解),则:

  1. 先找出一个区间 [a, b],使得f(a)与f(b)异号。根据介值定理,这个区间内一定包含着方程序的根。
  2. 求该区间的中点 m = \frac{a+b}{2},并找出 f(m) 的值。
  3. f(m) 与 f(a) 正负号相同则取 [m, b] 为新的区间, 否则取 [a, m].
  4. 重复第2和第3步至理想精确度为止。
英语百科

Bisection method 二分法 (数学)

A few steps of the bisection method applied over the starting range [a1;b1]. The bigger red dot is the root of the function.

The bisection method in mathematics is a root-finding method that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. It is a very simple and robust method, but it is also relatively slow. Because of this, it is often used to obtain a rough approximation to a solution which is then used as a starting point for more rapidly converging methods. The method is also called the interval halving method, the binary search method, or the dichotomy method.

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