User:Shibatch/sandbox

Applying Newton's method to the equation $$(1/x^3) - a = 0$$ produces a method that converges to the cube root of 1/a:


 * $$x_{n+1} = \frac{1}{3} \left( 4x_n - ax_n^4 \right).$$

Then, an approximation of the cube root of a can be computed as $$ax_n^2$$. This method does not require a division.