Newton-Ralphson Method

iterative scheme for finding the zero of a function

1. guess
2. find the root of the tangent line as a new guess
3. go to 2 until convergence

$$\begin{array}{rl}{f}^{\prime }(x\_1)& =\frac{f(x\_1)-0}{x\_1-x\_2}\\ x\_2& =x\_1-\frac{f(x\_1)}{f^{\prime }(x\_1)}\\ & \dots \\ x^{(i+1)}& =x^{(i)}-\frac{f(x^{(i)})}{f^{\prime }(x^{(i)})}\end{array}$$