An Elimination Method to Solve Interval Polynomial Systems

TL;DR

This paper introduces a novel elimination method based on algebraic geometry concepts, specifically Groebner bases, to solve and analyze general interval polynomial systems, extending existing methods beyond linear cases.

Contribution

The paper presents a new elimination approach utilizing comprehensive Groebner systems for solving general interval polynomial systems, addressing a gap in current computational methods.

Findings

Effective in solving general interval polynomial systems

Maintains dependencies between interval coefficients

Demonstrates applicability through practical examples

Abstract

There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new elimination method to solve and analyse interval polynomial systems, in general case. This method is based on computational algebraic geometry concepts such as polynomial ideals and Groebner basis computation. Specially, we use the comprehensive Groebner system concept to keep the dependencies between interval coefficients. At the end of paper, we will state some applications of our method to evaluate its performance.