An Interval Newton Methods for Bounding Zeros of Polynomial Systems using B-Spline Expansion

Abstract

The purpose of this paper is to study a technique of finding the zeros of a nonlinear polynomial equations. Interval method can be used to obtain rigorous bounds on a roots in a given box. The proposed algorithms for obtaining the roots of the polynomial system is based on the following technique:

1) transformation of the original nonlinear algebraic equations into polynomial B-spline form; 2) includes a pruning step using B-spline Newton operator.

We compare the performance of our proposed B-spline Newton operator with the interval Newton operator using two numerical examples. The results of the tests show the superiority of the proposed algorithm, in terms of selected performance metrics.