Una Solución al Método de Newton-Raphson de Orden Cuadrático para Acelerar la Convergencia de Algoritmos Iterativos de Varias Variables

Abstract

Currently, it is sought to reduce the execution times of the iterative algorithms that are used in the optimizations that help society to find roots, maximums and minimums in solutions to prescriptive models. These algorithms are born as the responses of applied mathematics to be executed in any type of computer, predominantly mobile computers, which due to their limited resources, we are forced to reduce the time spent in the processor to seek convergence in function problems of several variables. Some algorithms only manage to exploit polynomials of degree 1, leaving out some non-linear solutions, which can accelerate convergence by approaching the search for the root of a polynomial function of degree 2. This work aims to demonstrate the conditions for this type of models to converge in 1-variable and 2-variable models, being able to determine a generality about this type of expressions. Finally, it proceeds to experiment with a simple programming tool such as a spreadsheet, to demonstrate that there is speed in the convergence towards the root of the function.