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[it-uh-rey-shuh n] /ˌɪt əˈreɪ ʃən/
the act of repeating; a repetition.
  1. Also called successive approximation. a problem-solving or computational method in which a succession of approximations, each building on the one preceding, is used to achieve a desired degree of accuracy.
  2. an instance of the use of this method.
  1. a repetition of a statement or statements in a program.
  2. a different version of an existing data set, software program, hardware device, etc.:
    A new iteration of the data will be released next month.
a different form or version of something:
He designed the previous iteration of our logo.
Origin of iteration
late Middle English
1425-75; late Middle English < Latin iterātiōn-, stem of iterātiō; see iterate, -ion Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2017.
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Word Origin and History for iteration

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).

Online Etymology Dictionary, © 2010 Douglas Harper
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iteration in Technology
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
The Free On-line Dictionary of Computing, © Denis Howe 2010
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