asymptotic function (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/ˌeɪsɪmˈtɒtɪk ˈfʌŋkʃən/

Meaning and Usage

An asymptotic function is a function that describes the behavior of a quantity in relation to another quantity, typically as one approaches a limit, especially infinity. In mathematics and computer science, asymptotic functions are often used to analyze the performance and complexity of algorithms. The term is commonly used in the context of Big O notation, which helps describe the upper bounds of the runtime or space complexity of algorithms as the input size approaches infinity.

• Frequency of Use: The term "asymptotic function" is more frequently used in written contexts, particularly in academic papers, textbooks, and technical documentation related to mathematics, computer science, and statistics.

Example Sentences

1. The researchers utilized the asymptotic function to determine the efficiency of their algorithm as the input size grew.

2. Исследователи использовали асимптотическую функцию, чтобы определить эффективность своего алгоритма по мере увеличения размера входных данных.

3. In this study, we will analyze the asymptotic function behaviors of several different sorting algorithms.

4. В этом исследовании мы проанализируем поведения асимптотических функций нескольких различных алгоритмов сортировки.

5. The asymptotic function gives us a way to predict performance limits without manual calculations.

6. Асимптотическая функция дает нам способ предсказать предельные значения производительности без ручных расчетов.

Idiomatic Expressions

The term "asymptotic function" is not commonly used in idiomatic expressions, as it is a technical term primarily found in specific academic and professional contexts. However, related concepts in asymptotic analysis do lend themselves to expressions within mathematics and computer science.

Example Sentences with Related Concepts

1. The algorithm approaches linear time complexity asymptotically, which is a significant improvement.

2. Алгоритм приближается к линейной сложности времени асимптотически, что является значительным улучшением.

3. As the sample size increases, the results become asymptotically normal due to the Central Limit Theorem.

4. По мере увеличения размера выборки результаты становятся асимптотически нормальными благодаря центральной предельной теореме.

5. We can say that the performance of this function scales asymptotically with the input data size.

6. Мы можем сказать, что производительность этой функции асимптотически масштабируется с размером входных данных.

Etymology

The term "asymptotic" comes from the Greek word "asumptotos," which means "not falling together." It combines the prefix "a-" (without) and the root "symptotos" (falling together), implying that the function does not converge to a particular value but behaves predictively as it approaches a limit. The word "function" comes from the Latin "functio," meaning "performance, execution."

Synonyms and Antonyms

• Synonyms:
• Approximating function
• Asymptote-related function

• Limit function

• Antonyms:

• Exact function
• Non-asymptotic function

The term "asymptotic function" is critical in fields where limits and performance analysis are of interest, particularly in the study of algorithms and complex systems. Its usage underlines the importance of understanding behavior at scale, making it a foundational concept in both theoretical and applied mathematics.