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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“I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”
—Isaac Newton (1642–1727)
“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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