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Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, [1] Edmund Landau, [2] and others, collectively called Bachmann–Landau notation or asymptotic notation.
Big O notation – Describes limiting behavior of a function; Leading-order term – Terms in a mathematical expression with the largest order of magnitude; Method of dominant balance – Solution of a simplified form of an equation; Method of matched asymptotic expansions
an asymptotic dominant notation related to big O notation; in probability theory, a possible outcome of an experiment; the arithmetic function counting a number's distinct prime factors; the symbol ϖ, a graphic variant of π, is sometimes construed as omega with a bar over it; see π
4. Written as a function of another function, it is used for comparing the asymptotic growth of two functions. See Big O notation § Related asymptotic notations. 5. In number theory, may denote the prime omega function. That is, () is the number of distinct prime factors of the integer n.
It is a term commonly encountered in computer science research as a result of widespread use of big-O notation. More formally, an algorithm is asymptotically optimal with respect to a particular resource if the problem has been proven to require Ω(f(n)) of that resource, and the algorithm has been proven to use only O(f(n)).
In theoretical analysis of algorithms it is common to estimate their complexity in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily large input. Big O notation, Big-omega notation and Big-theta notation are used to this end. [2]
Big Omega function (disambiguation), various arithmetic functions in number theory; Big O notation, asymptotic behavior in mathematics and computing Time complexity in computer science, whose functions are commonly expressed in big O notation
In formal mathematics, rates of convergence and orders of convergence are often described comparatively using asymptotic notation commonly called "big O notation," which can be used to encompass both of the prior conventions; this is an application of asymptotic analysis.