Nth root algorithm: Difference between revisions

Revision as of 07:44, 20 February 2008

Revision as of 07:48, 20 February 2008

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(for integer ''n'' there are ''n'' distinct [[complex number|complex]] solutions to this equation if <math>A > 0</math>, but only one is positive and real).

There is a very fast-[[convergence|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>