求解区间多项式组的消元法
An Elimination Method to Solve Interval Polynomial Systems
摘要：
在区间计算的背景下，有几种有效的方法来求解线性区间多项式系统，然而，区间多项式系统的一般情况还没有被覆盖。本文介绍一种新的消元法，用于一般情况下区间多项式方程组的求解和分析。这种方法是基于计算代数几何概念，如多项式理想和Groebner基础计算。特别地，我们使用综合Groebner系统的概念来保持区间系数之间的依赖性。在文章的最后，我们将陈述我们的方法来评估其性能的一些应用。
英文摘要：
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.
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