A Theory and an Algorithm of Approximate Groebner Basis
A Theory and an Algorithm of Approximate Groebner Basis
复制标题
近似Groebner基的理论和算法
DOI：
10.1109/synasc.2011.12
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Tateaki Sasaki
中科院分区：
文献类型：
--
作者：
Sumi;H;Sato Y;Harihara S;Tateaki Sasaki
本文讨论系数为浮点数的多项式。对于这类多项式，传统的理想概念被打破，我们首先定义了“近似理想”的概念，然后引入“保精度约简”的概念，定义了近似Groebner基，并给出了计算近似Groebner基的算法。我们证明了几个表现近似Groebner基基本性质的定理。该算法已经实现，并通过有指导意义的例子对近似Groebner基进行了具体的说明。
In this paper, we treat polynomials with coefficients of floating-point numbers. The conventional concept of ideal breaks down for such polynomials, and we first define a concept of "approximate ideal''. Then, introducing "accuracy-guarding reductions'', we define approximate Groebner bases and give an algorithm for computing the approximate Groebner bases. We prove several theorems showing basic properties of approximate Groebner bases. The algorithm has been implemented, and we explain the approximate Groebner bases concretely by instructive examples.