This method was named after Sir Isaac Newton and Joseph Raphson. It begins with a function f defined over real numbers, its derivative f′, and an initial guess x0 for the root of f. The solution comes to a stop when the function satisfies the assumptions made in the derivation of the formula and the initial guess is close.
The General Newton Raphson Method Formula is:
- Compute the values of f(x) and f′(x) for a given initial x.
- While the ratio of f(x) and f′(x) is greater than allowed error ϵ,xn+1=xn–f(xn)f′(xn)For all values from 0 to n.