iteration

Webster's Dictionary (1913)

Origin: L. iteratio.

1. Recital or performance a second time; repetition. Francis, Baron Verulam Bacon

What needs this iteration, woman?— William Shakespeare

2. Computers The execution of a statement or series of statements in a loop which is repeated in a computer program; as, at each iteration, the counter is incremented by 2.

Webster’s Revised Unabridged Dictionary (1913), from GCIDE 0.54 · with additions: GCIDE editors

Free On-line Dictionary of Computing

<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 a loop, 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)