Next generation computational method with cubic convergence

Abstract

Ram U. Verma (2013) invented several classes of the next generation computational methods, which were established on the Graph zooming principle for graphs of the functions involved after each derivative procedure. In this paper, we establish the cubic convergence rate for the following Next Generation Computational Method: For n = 0, 1, 2, · · ·, xn+1 = xn - f(xn)/f?(x0), where x0 is an initial point and and f is a real-valued continuously differentiable function with f?(xn) ? 0. We shall use more frequently an abbreviation of "Next Generation Computational Method" as "NGC method" throughout this paper and beyond.