The structure of polynomial ideals and Grobner bases
SIAM Journal on Computing
“One sugar cube, please” or selection strategies in the Buchberger algorithm
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
An algorithm to compute floating point Gro¨bner bases
Proceedings of the Maple summer workshop and symposium on Mathematical computation with Maple V : ideas and applications: ideas and applications
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
On the stability of Groübner bases under specializations
Journal of Symbolic Computation
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
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 simple algorithm to compute comprehensive Gröbner bases using Gröbner bases
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Computing floating-point gröbner bases stably
Proceedings of the 2007 international workshop on Symbolic-numeric computation
A speed-up of the algorithm for computing comprehensive Gröbner systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Survey paper: Structured low-rank approximation and its applications
Automatica (Journal of IFAC)
Floating-Point Gröbner Basis Computation with Ill-conditionedness Estimation
Computer Mathematics
A Study on Gröbner Basis with Inexact Input
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Fast optimal three view triangulation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
A new algorithm for computing comprehensive Gröbner systems
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Gröbner bases for polynomial systems with parameters
Journal of Symbolic Computation
F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
Journal of Symbolic Computation
Term cancellations in computing floating-point Gröbner bases
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Artificial discontinuities of single-parametric Gröbner bases
Journal of Symbolic Computation
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There are several preliminary definitions for a Gröbner basis with inexact input since computing such a basis is one of the challenging problems in symbolic-numeric computations for several decades. A structured Gröbner basis is such a basis defined from the data mining point of view: how to extract a meaningful result from the given inexact input when the amount of noise is not small or we do not have enough information about the input. However, the known algorithm needs a suitable (unknown) information on terms required for a variant of the Buchberger algorithm. In this paper, we introduce an improved version of the algorithm that does not need any extra information in advance.