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asymptotic analysis : ウィキペディア英語版
asymptotic analysis

In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has applications across science. Examples are
* In applied mathematics, asymptotic analysis is used to build numerical methods to approximate equation solutions.
* in computer science in the analysis of algorithms, considering the performance of algorithms when applied to very large input datasets.
* the behavior of physical systems when they are very large, an example being Statistical mechanics.
* in accident analysis when identifying the causation of crash through count modeling with large number of crash counts in a given time and space.
The simplest example, when considering a function ''f''(''n''), is when there is a need to describe its properties as becomes very large. Thus, if , the term 3 becomes insignificant compared to 2, when is very large. The function ''f''(''n'') is said to be "asymptotically equivalent to ''n''2 as → ∞", and this is written symbolically as .
== Definition ==
Formally, given functions and of a natural number variable , one defines a binary relation
:f \sim g \quad (\text n\to\infty)
if and only if (according to Erdelyi, 1956)
:\lim_ \frac = 1 ~.
This relation is an equivalence relation on the set of functions of . The equivalence class of informally consists of all functions which are approximately equal to in a relative sense, in the limit.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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