nth Root Algorithm - Derivation From Newton's Method

Derivation From Newton's Method

Newton's method is a method for finding a zero of a function f(x). The general iteration scheme is:

  1. Make an initial guess
  2. Set
  3. Repeat step 2 until the desired precision is reached.

The nth root problem can be viewed as searching for a zero of the function

So the derivative is

and the iteration rule is

leading to the general nth root algorithm.

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