Title :
A Theory and an Algorithm of Approximate Gröbner Bases
Author_Institution :
Univ. of Tsukuba, Tsukuba, Japan
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;
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
DOI :
10.1109/SYNASC.2011.12
