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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The marble index of a mind for ever
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“Traditional scientific method has always been at the very best 20-20 hindsight. It’s good for seeing where you’ve been. It’s good for testing the truth of what you think you know, but it can’t tell you where you ought to go.”
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