The Newton-Raphson Method is an iterative method used to find the roots of a given equation. It is commonly used in numerical analysis and is named after its inventors, Sir Isaac Newton and Joseph Raphson.
The method involves using an initial guess for the root and then repeatedly using an iteration formula to refine the guess until the desired level of accuracy is achieved. The iteration formula is based on the tangent line to the curve at the current guess for the root.
The iteration formula is given by: xn+1 = xn - f(xn) / f'(xn), where xn is the current guess for the root, f(xn) is the value of the function at xn, and f'(xn) is the derivative of the function at xn.
The Newton-Raphson Method is a very efficient method for finding roots of equations. It typically converges faster than other methods and can work with a wide range of functions. It also allows for a high level of accuracy to be achieved with relatively few iterations.
Yes, there are some limitations to this method. It may fail to converge if the initial guess is too far from the actual root or if the function has multiple roots. It also requires the calculation of the derivative, which can be difficult for some functions.