V2EX numerical-stability

Numerical Stability

Definition / 释义

数值稳定性:指一种数值算法在计算过程中面对舍入误差、截断误差等不可避免的小误差时,是否会让误差被控制在可接受范围内,而不是被逐步放大到影响结果可靠性的程度。(该术语也常与“问题的条件数/condition”一起讨论:算法稳定不等于问题本身好算。)

Pronunciation / 发音(IPA)

/numrkl stblti/

Examples / 例句

A stable algorithm gives reliable results even with rounding errors.
数值稳定的算法即使存在舍入误差,也能给出可靠结果。

When solving a linear system, checking numerical stability helps prevent small floatingpoint errors from growing into large inaccuracies, especially for illconditioned matrices.
在求解线性方程组时,评估数值稳定性可以避免微小的浮点误差被放大成严重偏差,尤其当矩阵病态(illconditioned)时更为重要。

Etymology / 词源

numerical 源自拉丁语 numerus(“数字、数量”),经由法语进入英语,表示“与数字/数值有关的”。stability 来自拉语 stabilis(“稳固的”),表示“稳定性”。合起来的 numerical stability 是数值分析领域的核心概念,用来描述“计算过程是否稳健”。

Related Words / 相关词汇

Literary Works / 文献与作品中的用例

  • Accuracy and Stability of Numerical Algorithms(Nicholas J. Higham)
  • Numerical Linear Algebra(Lloyd N. Trefethen & David Bau III)
  • Matrix Computations(Gene H. Golub & Charles F. Van Loan)
  • Numerical Recipes: The Art of Scientific Computing(Press, Teukolsky, Vetterling & Flannery)
  • Scientific Computing: An Introductory Survey(Michael T. Heath)
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