# Iteration

[it-uh-rey-shuh n] /ˌɪt əˈreɪ ʃən/

**noun**

1.

the act of repeating; a repetition.

2.

Mathematics.

3.

Computers.

4.

a different form or version of something:

He designed the previous iteration of our logo.

n.

late 15c., from Latin iterationem (nominative iteratio) “repetition,” **noun** of action from past participle stem of iterare “do again, repeat,” from iterum “again,” from PIE *i-tero-, from pronomial root *i- (see yon).

programming

Repetition of a sequence of instructions. A fundamental part of many algorithms. Iteration is characterised by a set of initial conditions, an iterative step and a termination condition.

A well known example of iteration in mathematics is Newton-Raphson iteration. Iteration in programs is expressed using loops, e.g. in C:

new_x = n/2; do x = new_x; new_x = 0.5 * (x + n/x); while (abs(new_x-x) > epsilon);

Iteration can be expressed in functional languages using recursion:

solve x n = if abs(new_x-x) > epsilon then solve new_x n else new_x where new_x = 0.5 * (x + n/x)

solve n/2 n

(1998-04-04)

Tagged: i

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