V2EX bisection method

Bisection Method

释义 Definition

二分法(也称“二分法求根”):一种用于求解方程 \(f(x)=0\) 的数值方法。它要求在区间 \([a,b]\) 上 \(f(a)\) 与 \(f(b)\) 异号(即根被“夹住”),然后不断取中点把区间对半缩小,从而逐步逼近根。优点是稳定、必收敛(在条件满足时),缺点是收敛速度较慢

发音 Pronunciation (IPA)

/baskn mθd/

例句 Examples

The bisection method finds a root by repeatedly halving an interval.
二分法通过不断把区间对半分来寻找方程的一个根。

Because the function changes sign on \([1,2]\), we can apply the bisection method to approximate the solution to \(f(x)=0\) within a chosen tolerance.
因为函数在区间 \([1,2]\) 上发生变号,我们可以使用二分法在给定误差范围内近似求出 \(f(x)=0\) 的解。

词源 Etymology

bisection 来自拉丁语词根:bi-(“二、两次”)+ section(“切开、分割”),字面意思是“切成两半”。method 源自希腊语 methodo,表示“追求知识的途径/方法”。合起来就是“通过不断对半分割来求解的办法”。

相关词 Related Words

文献与作品 Literary / Notable Works

  • Numerical Recipes: The Art of Scientific Computing(Press, Teukolsky, Vetterling, Flannery) 介绍并对比多种求根法,包括二分法(bracketing methods)。
  • Numerical Analysis(Burden & Faires) 以标准教材方式系统讲解二分法的收敛性与误差界。
  • An Introduction to Numerical Analysis(Kendall Atkinson) 在非线性方程求解章节中讨论二分法及其理论基础。
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