Root finding Algorithm
Newton's Method¶
Basic iterative method to find numerically approximate the roots of a real-valued function. The method starts with an initial guess of the root \(x_{0}\), the iteratively computes:
\[
x_{n+1}=x_{n}-\frac{f(x_{n})}{f^{\prime}(x_{n})}
\]
The point \(x_{n+1}\) is the x-axis intercept of the tangent \(f^{\prime}(x_{n})\) and is an increasingly accurate approximation of the functions root.