Asymptotic Analysis

In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has applications across science. Examples are

• 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.
• 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 is, when considering a function f(n), there is a need to describe its properties when n becomes very large. Thus, if f(n) = n2+3n, the term 3n becomes insignificant compared to n2 when n is very large. The function "f(n) is said to be asymptotically equivalent to n2 as n → ∞", and this is written symbolically as f(n) ~ n2.