asymptotic

简明释义

英[æsɪmpˈtɒtɪk]美[æsɪmpˈtɑːtɪk]

adj. 渐近的；渐近线的

英英释义

单词用法

同义词

反义词

例句

1.They can handle the prediction, filtering and smoothing problems in a unified frame work, and have asymptotic stability.

它们可统一处理，滤波，平滑和预报问题，且具有渐近稳定性。

2.These he called asymptotic solutions.

他把这些解叫作渐近解。

3.Its convergence and asymptotic optimality are proved strictly.

证明了它的收敛性和渐近最优性。

4.The concept of stability shows asymptotic behaviors of a system.

系统稳定性的概念，是用来刻画系统运动的渐近性质的。

5.Asymptotic noon, buy flowers to people more.

渐近中午，买花的人也多了。

6.It is shown that there is still an asymptotic perfect security of quantum key distribution under this attack strategy.

理论计算证明了量子密钥分配协议在这种攻击策略下仍具有足够的安全性。

7.In addition, we consider the asymptotic stability of continuous linear time-invariable systems.

同时，考虑了连续时间线性时不变系统的渐近稳定性问题。

8.In this paper we will give an algorithm for designing GFSR sequences which satisfy the asymptotic randomness approximately.

本文中，我们将给出一种设计GFSR序列的算法，所产生的序列近似地满足渐近随机性。

9.According to the equation of asymptotic curves, a family of nonlinear asymptotic curves are given to the principal normal surface.

根据渐近曲线的方程，具体给出主法线曲面的一族非直线的渐近曲线。

10.In statistics, the asymptotic 渐近的 behavior of an estimator describes its properties as the sample size approaches infinity.

在统计学中，估计量的渐近的行为描述了其在样本量趋向无穷大时的性质。

11.The asymptotic 渐近的 analysis of algorithms helps to determine their efficiency in terms of time complexity.

算法的渐近的分析有助于确定它们在时间复杂度方面的效率。

12.As the input size grows, the asymptotic 渐近的 performance of the sorting algorithm becomes more relevant.

随着输入大小的增长，排序算法的渐近的性能变得更加重要。

13.The asymptotic 渐近的 distribution of the sample mean is normally assumed under the Central Limit Theorem.

在中心极限定理下，样本均值的渐近的分布通常被假设为正态分布。

14.In physics, the asymptotic 渐近的 behavior of a particle's trajectory can be studied using differential equations.

在物理学中，可以使用微分方程研究粒子轨迹的渐近的行为。

作文

In the field of mathematics and statistics, the term asymptotic refers to the behavior of functions as they approach a certain limit, often as the input values grow infinitely large. This concept is crucial in various applications, including algorithm analysis, where it helps in understanding the efficiency of algorithms as the size of the input increases. For instance, when we analyze the time complexity of an algorithm, we often express its performance using asymptotic notation, such as Big O notation, which provides a high-level description of the algorithm's growth rate relative to the input size. The idea of asymptotic behavior allows mathematicians and computer scientists to simplify complex problems by focusing on the dominant factors that influence growth. For example, if an algorithm has a time complexity of O(n^2), this indicates that as the input size n becomes very large, the execution time will grow quadratically. However, for small input sizes, other factors may have a more significant impact on performance, but these become less relevant as n increases. Understanding asymptotic behavior is not limited to theoretical applications; it has practical implications as well. In real-world scenarios, software developers must consider how their code performs under various conditions. By leveraging asymptotic analysis, they can make informed decisions about which algorithms to implement, ensuring that their applications remain efficient and responsive even as user demands increase. Moreover, the concept of asymptotic behavior extends beyond computer science into other disciplines such as physics and economics. In physics, for instance, the asymptotic behavior of a system can reveal insights into its stability and long-term dynamics. Similarly, in economics, understanding how certain variables behave as they approach equilibrium can inform policy decisions and economic modeling. To illustrate the importance of asymptotic analysis, consider the comparison between two sorting algorithms: QuickSort and Bubble Sort. QuickSort has an average-case time complexity of O(n log n), while Bubble Sort has a time complexity of O(n^2). As the size of the data set increases, the difference in their asymptotic behavior becomes evident. For small data sets, Bubble Sort might perform adequately, but as the data size grows, QuickSort's efficiency will significantly outperform Bubble Sort, making it the preferred choice in most scenarios. In conclusion, the term asymptotic encapsulates a fundamental concept that aids in understanding the efficiency and behavior of functions in various fields. Whether in mathematics, computer science, physics, or economics, asymptotic analysis provides a framework for evaluating performance and making strategic decisions based on growth patterns. As we continue to encounter increasingly complex systems and data sets, mastering the concept of asymptotic behavior will be essential for anyone looking to thrive in these domains.

在数学和统计学领域，术语asymptotic指的是函数在接近某个极限时的行为，通常是当输入值无限增大时。这一概念在各种应用中至关重要，包括算法分析，它有助于理解算法在输入规模增加时的效率。例如，当我们分析一个算法的时间复杂度时，我们通常使用asymptotic符号来表达其性能，比如大O符号，它提供了算法相对于输入规模的增长率的高层次描述。 Asymptotic行为的思想使数学家和计算机科学家能够通过关注影响增长的主导因素来简化复杂问题。例如，如果一个算法的时间复杂度为O(n^2)，这表明当输入规模n变得非常大时，执行时间将以平方的方式增长。然而，对于小输入规模，其他因素可能对性能有更大的影响，但随着n的增加，这些因素变得不那么相关。 理解asymptotic行为不仅限于理论应用；它也具有实际意义。在现实世界的场景中，软件开发人员必须考虑他们的代码在各种条件下的表现。通过利用asymptotic分析，他们可以做出明智的决策，选择实现哪些算法，从而确保他们的应用程序即使在用户需求增加时也能保持高效和响应。 此外，asymptotic行为的概念超越了计算机科学，扩展到物理学和经济学等其他学科。在物理学中，例如，一个系统的asymptotic行为可以揭示其稳定性和长期动态的见解。同样，在经济学中，理解某些变量在接近平衡时的行为可以为政策决策和经济建模提供信息。 为了说明asymptotic分析的重要性，考虑比较两种排序算法：快速排序和冒泡排序。快速排序的平均时间复杂度为O(n log n)，而冒泡排序的时间复杂度为O(n^2)。随着数据集大小的增加，它们的asymptotic行为的差异变得明显。对于小数据集，冒泡排序可能表现得还不错，但随着数据规模的增长，快速排序的效率将显著优于冒泡排序，使其在大多数场景中成为首选。 总之，术语asymptotic概括了一个基本概念，有助于理解各个领域中函数的效率和行为。无论是在数学、计算机科学、物理学还是经济学中，asymptotic分析提供了评估性能和根据增长模式做出战略决策的框架。随着我们继续遇到越来越复杂的系统和数据集，掌握asymptotic行为的概念对于任何希望在这些领域中蓬勃发展的人来说都是必不可少的。