Table of Contents
ISRN Computational Mathematics
Volume 2013 (2013), Article ID 352806, 12 pages
http://dx.doi.org/10.1155/2013/352806
Research Article

Approximate Gröbner Bases, Overdetermined Polynomial Systems, and Approximate GCDs

Wolfram Research, Kernal Development Group, 100 Trade Center Drive, Champaign, IL 61820, USA

Received 6 November 2012; Accepted 29 November 2012

Academic Editors: R. Joan Arinyo, M. Ogihara, and Y. Peng

Copyright © 2013 Daniel Lichtblau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss computation of Gröbner bases using approximate arithmetic for coefficients. We show how certain considerations of tolerance, corresponding roughly to absolute and relative error from numeric computation, allow us to obtain good approximate solutions to problems that are overdetermined. We provide examples of solving overdetermined systems of polynomial equations. As a secondary feature we show handling of approximate polynomial GCD computations, using benchmarks from the literature.