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Numerical computation of Gröbner bases

By Aleksey Kondratyev, Hans J. Stetter and Franz Winkler

Abstract

In this paper we deal with the problem of numerical computation of Gröbner bases of zero-dimensional polynomial systems. It is well known that the computation of a Gröbner basis cannot be generally executed in floating-point arithmetic by a standard approach. This, however, would be highly desirable for practical applications. We present an approach for computing Gröbner bases numerically. It is an elaboration of the idea of a stabilized Gröbner basis computation initially proposed by Hans Stetter. Our implementation of the algorithm based on the presented results is available online

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.184.1675
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