Iteration in mathematics may refer to the process of iterating a function, or to the techniques used in iterative methods for solving numerical problems.
Computing
Iteration in computing is the repetition of a process within a computer program. It can be used both as a general term, synonymous with repetition, and to describe a specific form of repetition with a mutable state.
When used in the first sense, recursion is an example of "iteration", but typically using a "recursive notation", which is typically not the case for "iteration".
However, when used in the second (more restricted) sense, iteration describes the style of programming used in imperative programming languages. This contrasts with recursion, which has a more declarative approach.
Here is an example of iteration, in imperative pseudocode:
var i, a := 0 "// initialize a before iteration" for i from 1 to 3 { "// loop three times" a := a + i "// increment a by the current value of i" } print a "// the number 6 is printed"
In this program fragment, the value of the variable "i" changes over time, taking the values 1, 2 and 3. This changing value—or "mutable state"—is characteristic of iteration.
Iteration can be approximated using recursive techniques in functional programming languages. The following example is in Scheme. Note that the following is recursive (a special case of iteration) because the definition of "how to iterate", the iter function, calls itself in order to solve the problem instance. Specifically it uses tail recursion, which is properly supported in languages like Scheme so it does not use large amounts of stack space.(define (sum n) (define (iter n i) (if (= n 1) i (iter (- n 1)(+ n i)))) (iter n 1))
An iterator is an object that wraps iteration.
Project management
Iterations in a project context may refer to the technique of developing and delivering incremental components of business functionality. This is most often associated with agile software development, but could potentially be any material. A single iteration results in one or more bite-sized but complete packages of project work that can perform some tangible business function. Multiple iterations recurse to create a fully integrated product. This is often compared with the waterfall model approach.
ee also
*Iterator *For loop *While loop *Iterative and incremental development *Iterated function
Iteration — (von lat. iterare ,wiederholen‘) wird als Begriff in mehreren Anwendungsbereichen mit unterschiedlicher Bedeutung verwendet: Inhaltsverzeichnis 1 Numerische Mathematik 1.1 Anwendung der Methode 1.2 Beispiel: Bestimmung von Nullstellen einer… … Deutsch Wikipedia
itération — [ iterasjɔ̃ ] n. f. • 1488; lat. iteratio, de iterare 1 ♦ Didact. Répétition. 2 ♦ Math. Méthode de résolution d une équation par approximations successives (⇒ récurrence). 3 ♦ Psychiatr. Répétition involontaire et inutile d un même acte moteur ou … Encyclopédie Universelle
Iteration — Itération Une itération d un Pentagone En mathématiques, une itération désigne l action de répéter un processus. Le calcul itératif, permet l application à des équations récursives. Le terme « itération » vient du verbe latin iterare… … Wikipédia en Français
Iteration — It er*a tion, n. [L. iteratio.] 1. Recital or performance a second time; repetition. Bacon. [1913 Webster] What needs this iteration, woman? Shak. [1913 Webster] 2. (Computers) The execution of a statement or series of statements in a loop which… … The Collaborative International Dictionary of English
Iteration — (lat.), s. Reïteration … Kleines Konversations-Lexikon
Iteration — Iteration, lat. dtsch., Wiederholung; iterativ, wiederholend; Iterativum, = Frequentativum, lat., ein Zeitwort, das eine Wiederholung der Handlung anzeigt … Herders Conversations-Lexikon
iteration — index narration, recital, restatement Burton s Legal Thesaurus. William C. Burton. 2006 … Law dictionary
iteration — Iteration, Iteratio … Thresor de la langue françoyse
iteration — [it΄ər ənsit΄ər ā′shən] n. [ME < L iteratio] 1. an iterating or being iterated; repetition 2. something iterated: Also iterance [it΄ər əns] … English World dictionary
Iteration X — articleissues unreferenced=December 2007 notable=July 2008 in universe=July 2008The Iteration X are a convention of the Technoracy in the role playing game , a game by White Wolf using the World of Darkness setting. They are mostly concerned with … Wikipedia
