Finding the Solutions of Nonlinear Equation Systems from an Interval

Abstract

The paper describes an algorithm that determines the solutions of a n-dimensional nonlinear equation system within a given interval. The result is based on Semenov algorithm that isolates the solutions and improves upon it by introducing Kantorovich existence criterion. In Semenov algorithm the existence of the solution is decided by applying Newton method on each interval containing at most one solution. This article improves and completes the Semenov algorithm by determining the start iteration for each solution. With the computed start iteration the Newton method is applied to determine the solution with the precision ε. The Kantorovich error function E(k) is also computed for each iteration k. The paper contains numerical experiments.