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iteration

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iteration

In computing, a method of solving a problem by performing the same steps repeatedly until a certain condition is satisfied. For example, in one method of sorting, adjacent items are repeatedly exchanged until the data are in the required sequence.

iteration

In mathematics, method of solving equations by a series of approximations which approach the exact solution more and more closely. For example, to find the square root of N, start with a guess n1; calculate

N/n1 = x1

calculate

(n1 + x1)/2 = n2

calculate

N/n2 = x2

calculate

(n2 + x2)/2 = n3

The sequence n1, n2, n3 approaches the exact square root of N. Iterative methods are particularly suitable for work with computers and programmable calculators.



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Tulliver on these puzzling subjects during his rides on the gray horse; much turning of the head from side to side, as the scales dipped alternately; but the probable result was still out of sight, only to be reached through much hot argument and iteration in domestic and social life.
Nowhere, indeed, was any sign or suggestion of life except the barking of a distant dog, which, repeated with mechanical iteration, served rather to accentuate than dispel the loneliness of the scene.
He had never before seen a woman's lips and teeth which forced upon his mind with such persistent iteration the old Elizabethan simile of roses filled with snow.
 
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