Convergence Condition for the Newton-Raphson Method. Application in Real Polynomial Functions

Abstract

Juan Jorge Isaac Lopez

The Newton-Raphson method applies to the numerical calculation of the roots of Real functions, through successive approximations towards the Root of the function. The Newton-Raphson method has the drawback that it does not always converge. This work establishes the convergence condition of the Newton-Raphson method for Real functions in general; once the convergence condition is met, the method will always converge towards the Root of the function. In this work, the development of the application of the convergence condition is established to specially solve Real polynomial functions.

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