V2EX condition number

Condition Number

定义 Definition

条件数:在数值分析与线性代数中,用来衡量一个函数或矩阵在输入发生微小扰动时,输出会被放大多少的指标。条件数越大,问题越“病态”(对误差更敏感);条件数越小,越“良态”(更稳定)。常见于矩阵求解线性方程组、求逆、特征值计算等情境。(在矩阵情形下,常指某种范数下的条件数,如 2-范数条件数。)

例句 Examples

The condition number of this matrix is small, so the solution is stable.
这个矩阵的条件数很小,所以解是稳定的。

Because the condition number is extremely large, tiny measurement errors can cause huge changes in the computed result.
由于条件数极大,微小的测量误差也可能导致计算结果发生巨大的变化。

发音 Pronunciation (IPA)

/kndn nmbr/

词源 Etymology

“condition”源自拉丁语 condicio(条件、约定),强调“受哪些条件影响”;“number”源自拉丁语 numerus(数、数量)。合在一起,“condition number”字面意思是“衡量条件影响程度的数”,对应其在数值计算中“衡量对扰动敏感程度”的用途。

相关词 Related Words

文献与作品 Literary / Notable Works

  • Matrix Computations(Gene H. Golub & Charles F. Van Loan)系统讨论条件数与数值稳定性。
  • Numerical Linear Algebra(Lloyd N. Trefethen & David Bau III)以直观方式讲解条件数与误差放大。
  • Linear Algebra and Its Applications(Gilbert Strang)在矩阵与线性方程组章节中出现条件数概念。
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