Newton Iteration Method

newton.rb

#!/usr/bin/env ruby
 
# Created by ZHANG Hailong <[email protected]>
 
# Newton Iteration Method
 
# f(x) = X^2 - a = 0. Here a = 2.
# Xn+1 = Xn - (Xn^2 - 2) / 2Xn = Xn / 2 + 1 / Xn.
 
x0 = 1.0
n = 5
x = x0 / 2 + 1 / x0
 
(n - 1).times do
  x = x / 2 + 1 / x
end
 
puts x