nth root algorithm
Appearance
The principal nth root of a positive real number A, is the positive real solution of the equation . For a positive integer n there are n distinct complex solutions to this equation if , but only one is positive and real.
Using 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
See also
References
- Atkinson, Kendall E. (1989), An introduction to numerical analysis (2nd ed.), New York: Wiley, ISBN 0-471-62489-6.