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Approximate Gröbner Bases and Overdetermined Algebraic Systems
Author

Daniel Lichtblau
Organization: Wolfram Research, Inc.
Conference

ACA 2008
Conference location

RISC, Linz, Austria
Description

This is from a rpesentation at ACA 2008, RISC, Linz, Austria, July 2008. Session on Symbolic and Numeric Computation.

Abstract
We discuss computation of Gröbner bases using approximate arithmetic for coefficients. We show how certain considerations of tolerance, corresponding roughly to accuracy and precision 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.
Subjects

*Mathematica Technology > Kernel > Numerics
*Mathematica Technology > Programming > Symbolic Computation
*Mathematics > Algebra > Field and Ring Theory
*Mathematics > Algebra > Polynomials
Keywords

Groebner bases, symbolic-numeric computation, hybrid computation, approximate polynomial algebra
URL

http://www.risc.uni-linz.ac.at/about/conferences/aca2008/
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ACA2008_ApproximateGB_slides.pdf (62.6 KB) - PDF Document
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ApproximateGroebnerBases.pdf (65.8 KB) - PDF Document
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ACA2008_ApproximateGB_slides.nb (200.1 KB) - Mathematica Notebook
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ApproximateGroebnerBases.nb (202.8 KB) - Mathematica Notebook