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)

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