Approximate Gröbner Bases, Overdetermined Polynomial Systems, and Approximate GCDs. (21st March 2013)

• Record Type: Journal Article
• Authors: Lichtblau, Daniel
• Other Names: Joan Arinyo R. Academic Editor.; Ogihara M. Academic Editor.; Peng Y. Academic Editor.
• Is Part Of: ISRN computational mathematics. Volume 2013(2013)
• Publication Date: 2013-03-21
• Subjects: Numerical analysis -- Periodicals; Mathematics -- Data processing -- Periodicals; Mathematics -- Data processing; Numerical analysis; Electronic journals; Periodicals; 510
• DOI: 10.1155/2013/352806
• Languages: English
• ISSNs: 2090-7842

Abstract

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.