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:
- Make an initial guess
- Set
- 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.
Read more about this topic: nth Root Algorithm
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