Numerical stability and stabilization of Groebner basis computation

  • Authors:

  • Carlo Traverso;Alberto Zanoni

  • Affiliations:

  • Università di Pisa, Via Buonarroti 2, I-56127 Pisa, Italy;Università di Firenze, V.le Morgagni 67/A I-50134 Firenze, Italy

  • Venue:
  • Proceedings of the 2002 international symposium on Symbolic and algebraic computation
  • Year:
  • 2002

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Abstract

In this paper we consider the problem of the use of approximate arithmetics in Gröbner basis computation. This is useful to reduce the cost of integer arithmetic, but is especially necessary for overdetermined systems whose coefficients are only approximately known.We report on some numerical experiments, that show that the intrinsic instability of the problem is high but not such as to make the problem unmanageable, and that there is space to improve the numerical stability of the algorithms.We suggest some algorithms to deal with the case of overdetermined and unstable systems.