Iteration

Pronunciation: /ˌɪ təˈreɪ ʃən/ ?
Graph of a function that has a value of 2 from negative infinity to 1, and a value of 1 from 1 to infinity with a jump discontinuity at x=1.
Figure 1: Jump discontinuity

An iteration is a step in a repeating algorithm. For example, to find the square root of 37, one can note that 37 is close to 36, so the square root of 37 is close to 6, the square root of 36.

IterationCalculations
137÷6 ≈ 6.16667; (6+6.16667)/2 = 6.08333
237÷6.08333 ≈ 6.08219; (6.08333+6.08219)/2 = 6.08276
337÷6.08276 ≈ 6.08277
Table 1: Iterations

The actual value of the square root of 37 is about 6.08276.

References

  1. iteration. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=iteration&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Harris, Simon; Ross, James . Beginning Algorithms, pp 15-42. Wrox, November 7, 2005. (Accessed: 2010-03-03).
  3. Michael Goodrich. Algorithm Design: Foundations, Analysis, and Internet Examples. Wiley, October 1, 2001. (Accessed: 2010-03-03).

Printed Resources

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Iteration. 2010-03-03. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/iteration.html.

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2008-09-16: Initial version (McAdams, David.)

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