SOLVING SYSTEM OF NONLINEAR EQUATIONS BY THE THIRD – ODER NEWTON – KRYLOV METHOD

Abstract

When solving problems in practice, constraints are often formulated as a system of nonlinear equations. The exact solution of these systems of equations is difficult, and there are even systems of equations for which we cannot find an exact solution. Therefore, the problem of approximate solution of this problem is very necessary. In this paper, we present solving the system of nonlinear equations by third-order Newton - Krylov method, and prove the convergence of iterative formula. This paper also presents some empirical results for the problem.