An Interval Newton Methods for bounding zeros of Polynomial Systems using B-spline expansion (2019)
Deepak Gawali
JCR. 2019: 652-665
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.
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