Nth root algorithm: Difference between revisions

Revision as of 13:04, 16 January 2014

Revision as of 09:51, 24 January 2014

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There is a very fast-[[Limit of a sequence|converging]] ''' ''n''th root algorithm''' for finding <math>\sqrt[n]{A}</math>:

#Make an initial guess <math>x_0</math>

#Set <math>x_{k+1} = \frac{1}{n} \left[{(n-1)x_k +\frac{A}{x_k^{n-1}}}\right]</math>. In practice we do <math> \Delta x_k = \frac{1}{n} \left[{\frac{A}{x_k^{n-1}}} - x_k\right]; x_{k+1} = x_{k} + \Delta x_k </math>.

#Repeat step 2 until the desired precision is reached, i.e. <math> | \Delta x_k | < \epsilon</math> .