Newton-Raphson Method
Newton-Raphson description
Newton-Raphson method is an iterative numerical technique used to finding approximate solutions to equations.
This is used to solve equations of the form \(f(x) = 0\) where \(f(x)\) is a real-valued function of a real variable.
Given an initial guess (\(x_0\)), the method iteratively refines this guess to get closer and closer to a root of the equation.
Formula
- The core formula for the Newton-Raphson methods is: \[ x_{n+1} = x_n-\dfrac{f(x_n)}{(f^\prime x_n)} \]
where:
\(x_{n+1}\) is the next approximation of the root
\(x_n\) is the current approximation of the root
\(f(x_n)\) is the value of the function at \(x_n\)
\(f^\prime x_n\) is the derivative (slope) of the function at \(x_n\)