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TitleNumerical Gröbner bases and syzygies: an interval approach
Author(s) Marco Bodrato, Alberto Zanoni
TypeArticle in Conference Proceedings
Abstract In Gröbner bases computation a general open question is how to guide
calculations coping with numerical coefficients and/or not exact
input data. It may happen that, due to error accumulation or
insufficient working precision, the result is not one theoretically
expects. The basis may have more or less polynomials, a different
number of solutions, a zero set with wrong multiplicity, and so on.
Augmenting precision we may overcome algorithmic errors, but we
don't know in advance how much it should be, and a trial-and-error
approach is often the only way. Coping with initial errors is an
even more difficult task. In this work the combined use of
syzygies and interval arithmetic is proposed as a technique to
decide at each critical point of the algorithm what to do.
Keywordsnumerical Gröbner bases, syzygies, intervals
Pages77 - 89
PublisherMIRTON, Timisoara, Romania
EditorD. Petcu, D. Zaharie, V. Negru, T. Jebelean
Translation No
Refereed Yes
BookSYNASC 2004 conference proceedings
Organization Department of Computer Science, West University, Timisoara, Romania
Institution Department of Computer Science, West University, Timisoara, Romania
ConferencenameSYNASC 2004