What is "asymptotic analysis"

n. (context mathematics English) Any of several methods for describing and analyzing the behaviour of a system at its limits

In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The method 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 very big 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.

A simple illustration, when considering a function , is when there is a need to describe its properties as becomes very large. Thus, if , the term 3 becomes insignificant compared to , when is very large. The function is said to be "asymptotically equivalent to as → ∞", and this is written symbolically as .