On finding leading to Newton Raphson’s improved method

Abstract: New iterative algorithms for finding the nth root of a positive number m, to any degree of accuracy, are discussed. The convergence of these methods is also analyzed and the factors affecting the rate of convergence are studied analytically, as well as graphically. The parameters involved in the iterative schemes are studied. Expressions are derived for the optimal values of these parameters. The rates of convergence of these new methods can be accelerated through these parameters, which prove to be much faster than the Newton Raphson method for finding in some cases. Several examples are given for clarity purposes. Also, numerical comparative study is made between the improved Newton Raphson’s method and the third order Halley’s method