V2EX asymptotic

Asymptotic

释义 Definition

渐近的;与渐近线有关的(常用于数学/统计/计算机科学中):指当某个变量趋近于某个值(常见为无穷大或某点)时,函数、序列或算法的行为/性质所呈现的趋势或近似形式。也常见于短语 asymptotic analysis(渐近分析)asymptotic behavior(渐近行为)

发音 Pronunciation

/smttk/

例句 Examples

Asymptotic behavior can be very different from small-number behavior.
渐近行为可能与小规模(小数值)情况下的表现非常不同。

The paper gives an asymptotic estimate of the algorithm’s running time as the input size grows.
这篇论文给出了当输入规模增大时该算法运行时间的渐近估计。

词源 Etymology

asymptotic 来自希腊语词根:**a-**(否定,“不”)+ **syn-**(“一起”)+ piptein(“落下/相遇”),与“渐近线(asymptote)”同源,原意可理解为“不会相遇的(线)”。在数学语境中延伸为“只会无限接近而不在有限范围内相交/相等”的性质,因此形成“渐近的”这一含义。

相关词 Related Words

文学与著作中的用例 Literary & Notable Works

  • Donald E. Knuth, The Art of Computer Programming(多处讨论算法的asymptotic复杂度与估计)
  • Thomas H. Cormen et al., Introduction to Algorithms(系统使用asymptotic记号与分析方法)
  • Walter Rudin, Principles of Mathematical Analysis(在极限与函数行为相关章节出现“asymptotic”及相关表述)
  • G. H. Hardy, A Course of Pure Mathematics(涉及函数/级数的渐近性质与估计)
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