Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function in the vicinity of a suspected root . Newton's method is sometimes also known as Newton's iteration , although in this work the latter term is reserved to the application of Newton's method for computing square roots . In Numerical Analysis, Newton’s method (also known as the Newton–Raphson method ), named after Sir Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. It is one example of a root-finding algorithm The Newton–Raphson method in one variable is implemented as follows: The method starts with a function f defined over the real numbers x , the function’s derivative f ′ , and an initial guess x 0 for a root of the function...