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Encyclopedia > Iteration

The word iteration is sometimes used in everyday English with a meaning virtually identical to repetition.


Mathematics

Iteration in mathematics is the technique used in iterative methods, described in a separate article. An iterative method attempts to solve a problem (for example an equation or system of equations) by finding successive approximations to the solution starting from an initial guess. ...


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. Look up Process in Wiktionary, the free dictionary Process (lat. ... The terms computer program, software program, applications program, system software, or just program are used to refer to either an executable program by both lay people and computer programmers or the collection of source code from which an executable program is created (eg, compiled). ... In computer science, an immutable object, as opposed to a mutable object, is a kind of object whose internal states cannot be modified. ...


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. A Sierpinski triangle —a confined recursion of triangles to form a geometric lattice. ...


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 an example of iteration, in imperative pseudocode: Pseudocodes can refer to the technique of using short codes, especially within the language with singular name Short Code, which was the first ever language developed for an electronic computing device. ...

 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: Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions. ... Scheme is a functional programming language and a dialect of Lisp. ...

 (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. In computer science, an iterator is an object allowing one to sequence through all of the elements or parts contained in some other object, typically a container or list. ...


See also


  Results from FactBites:
 
iteration - definition of iteration in Encyclopedia (226 words)
Iteration is the repetition of a process, typically within a computer program.
Confusingly, it can be used both as a general term, synonymous with repetition, and to describe a specific form of repetition with a mutable state.
An iterator is an object that wraps iteration.
  More results at FactBites »

 
 

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