Talk:Square root algorithms: Difference between revisions

Revision as of 16:08, 12 October 2010

Revision as of 23:22, 7 March 2011

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:The true root will lie between <math>x_n \!</math> and <math>\frac{S}{x_n}</math>. So when their absolute difference is less than the required value, then <math>x_n \!</math> (or better still <math>x_{n+1} \!</math>) is close enough. [[User:JRSpriggs|JRSpriggs]] 20:45, 30 November 2007 (UTC)

Convergence: The Babylonian method only converges for <math>S \ge 0</math>. For <math>S < 0</math> the series is [[Chaos theory|chaotic]], never converges, and is highly sensitive to both <math>S</math> and <math>x_0</math>. If you guess <math>x_0<0</math>, the series will converge to the negative root <math>-\sqrt{S}</math> [http://personal.bgsu.edu/~carother/babylon/Examples.html].

== Pell's equation ==