Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Stabilization of polynomial systems solving with Groebner bases
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Remarks on automatic algorithm stabilization
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Numerical stability and stabilization of Groebner basis computation
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
A complete symbolic-numeric linear method for camera pose determination
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Numerical Polynomial Algebra
Generalized normal forms and polynomial system solving
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Computing floating-point gröbner bases stably
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Minimum converging precision of the QR-factorization algorithm for real polynomial GCD
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Artificial discontinuities of single-parametric Gröbner bases
Journal of Symbolic Computation
Structures of precision losses in computing approximate Gröbner bases
Journal of Symbolic Computation
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The computation of approximate Grobner bases is reported to be highly unstable in the literature. Selecting a suitable length of floats is helpful for stabilizing this computation. In this paper, we present a method to compute such a suitable length of floats. We concentrate on a family of polynomial systems sharing the same support and study the relation between the lengths of floats and the coefficients of relevant polynomials. Then we give a reference length of floats for all the polynomial systems in the family. One feature of our method is that it need not utilize numerical algorithms of Grobner bases. Hence, our method can avoid the influence of the instabilities of the existing numerical algorithms and thus will be helpful for designing stable ones (e.g., stable Shirayanagi@?s algorithm). Experiments show that our method can work out reliable and reasonably large lengths of floats for most of the tested benchmarks.