|
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 : if and only if (according to Erdelyi, 1956) : 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）』 ■ウィキペディアで「Asymptotic analysis」の詳細全文を読む スポンサード リンク
|