THE SPEED OF CONVERGENCE OF THE THIRD – ODER NEWTON – KRYLOV METHOD

Abstract

In recent years, the approximate solution of the system of nonlinear equations has been studied by many scientists, especially the class of systems of nonlinear equations with a large number of equations. The third-order Newton - Krylov method solved these systems very well with the speed of cubed of convergence. The convergence of iterated formula has been proofed, however, its only has been confirmed by experiment. In this article, we will present the speed of convergence of the third-order Newton - Krylov method and give the proof for the speed of convergence of iterated formula simultaneously. Moreover, the article also presents a consult of experiment to proof for the speed of convergence of the Newton–Krylov method.