A Theory and an Algorithm of Approximate Gröbner Bases

Author

Sasaki, Tateaki

Author_Institution

Univ. of Tsukuba, Tsukuba, Japan

fYear

2011

fDate

26-29 Sept. 2011

Firstpage

23

Lastpage

30

Abstract

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.

Keywords

approximation theory; floating point arithmetic; polynomials; process algebra; accuracy-guarding reduction; approximate Gröbner bases; approximate ideal; floating-point number; polynomial; Accuracy; Approximation algorithms; Approximation methods; Argon; Polynomials; Systematics; Vectors; accuracy-guarding reduction; approximate Groebner basis; approximate ideal; floating-point Groebner basis; term cancellation;

fLanguage

English

Publisher

ieee

Conference_Titel

Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2011 13th International Symposium on

Conference_Location

Timisoara

Print_ISBN

978-1-4673-0207-4

Type

conf

DOI

10.1109/SYNASC.2011.12

Filename

6169497