Iteration

Pronunciation: /ˌɪ təˈreɪ ʃən/ Explain
Graph of a function that equals 2 on the range [-8,1] and equals 1 on the range (1,8]
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. Harris, Simon; Ross, James . Beginning Algorithms. pp 15-42. Wrox. November 7, 2005. Last Accessed 8/6/2018. Buy the book
  2. Michael Goodrich. Algorithm Design: Foundations, Analysis, and Internet Examples. Wiley. October 1, 2001. Last Accessed 8/6/2018. Buy the book

Cite this article as:

McAdams, David E. Iteration. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/iteration.html.

Image Credits

Revision History

8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
9/16/2008: Initial version. (McAdams, David E.)

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