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iteration - 4 dictionary results

it⋅er⋅a⋅tion

  [it-uh-rey-shuhn]
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–noun
1. the act of repeating; a repetition.
2. Mathematics.
a. 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.
b. an instance of the use of this method.
3. Computers. a repetition of a statement or statements in a program.
Origin:
1425–75; late ME < L iterātiōn-, s. of iterātiō; see iterate, -ion
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
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it·er·a·tion   (ĭt'ə-rā'shən)   
n.  
  1. The act or an instance of iterating; repetition.
  2. Mathematics A computational procedure in which a cycle of operations is repeated, often to approximate the desired result more closely.
  3. Computer Science
    1. The process of repeating a set of instructions a specified number of times or until a specific result is achieved.
    2. One cycle of a set of instructions to be repeated: After ten iterations, the program exited the loop.
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Iteration

It`er*a"tion\, n. [L. iteratio.] Recital or performance a second time; repetition. --Bacon.

What needs this iteration, woman? --Shak.
Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
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iteration 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)

The Free On-line Dictionary of Computing, © 1993-2007 Denis Howe
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