V2EX nondifferentiable

Nondifferentiable

Definition / 释义

(数学)不可微的;不可求导的:指函数在某一点(或某一区间)不存在导数,常见于出现“尖点、折点、拐角”或不够光滑的情况。(也常写作 non-differentiable

Pronunciation / 发音(IPA)

/nndfrnbl/

Examples / 例句

The function \(f(x)=|x|\) is nondifferentiable at \(x=0\).
函数 \(f(x)=|x|\) 在 \(x=0\) 处是不可微的。

Because the loss function is nondifferentiable at some points, the algorithm uses a subgradient method instead of ordinary gradient descent.
由于损失函数在某些点不可微,该算法使用次梯度方法而不是普通的梯度下降。

Etymology / 词源

由前缀 **non-**(表示“非、不”)+ differentiable(“可微的、可求导的”)构成。Differentiable 源自动词 differentiate(区分、求导),与拉丁语 differre(“分开、使不同”)相关;在数学语境中发展出“求微分/求导”的含义。

Related Words / 相关词

Notable Works / 文献与著作中的用例

  • Principles of Mathematical Analysis(Walter Rudin)在讨论可微性与反例时会涉及“不可微”情形。
  • Calculus(Michael Spivak)以经典例子(如绝对值函数、尖点等)说明不可微现象。
  • Convex Analysis(R. Tyrrell Rockafellar)在凸函数与优化理论中讨论不可微点与次梯度概念。
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