Iteration

Pronunciation: /ˌɪ.tərˈeɪ.ʃən/ Explain

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.

Iteration	Calculations
1	37 ÷ 6 ≈ 6.16667; (6 + 6.16667) / 2 = 6.08333
2	37 ÷ 6.08333 ≈ 6.08219; (6.08333 + 6.08219) / 2 = 6.08276
3	37 ÷ 6.08276 ≈ 6.08277
Table 1: Iterations

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

References

1. McAdams, David E.. All Math Words Dictionary, iteration. 2nd Classroom edition 20150108-4799968. pg 103. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Harris, Simon; Ross, James . Beginning Algorithms. pp 15-42. Wrox. November 7, 2005. Last Accessed 8/7/2018. Buy the book
3. Michael Goodrich. Algorithm Design: Foundations, Analysis, and Internet Examples. Wiley. October 1, 2001. Last Accessed 8/7/2018. Buy the book

Cite this article as:

McAdams, David E. Iteration. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/i/iteration.html.

Revision History

4/23/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
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.)