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.

Read more about Asymptotic Analysis:  Definition, Asymptotic Expansion, Use in Applied Mathematics, Method of Dominant Balance

Famous quotes containing the word analysis:

    The spider-mind acquires a faculty of memory, and, with it, a singular skill of analysis and synthesis, taking apart and putting together in different relations the meshes of its trap. Man had in the beginning no power of analysis or synthesis approaching that of the spider, or even of the honey-bee; but he had acute sensibility to the higher forces.
    Henry Brooks Adams (1838–1918)