Abstract
For a regular 0-dimensional system P of polynomials with numerical coefficients, its BKK-number m equals the number of its zeros, counting multiplicities. In this paper, I analyze how the knowledge of m may be used for the computation of a Gröbner basis or more generally a border basis of P. It is also shown how numerical stability may be preserved in such an approach, and how near-singular systems are recognized and handled. There remain a number of open questions which should stimulate further research.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Stetter, H.J. (2007). Proposal for the Algorithmic Use of the BKK-Number in the Algebraic Reduction of a O-dimensional Polynomial System. In: Wang, D., Zhi, L. (eds) Symbolic-Numeric Computation. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7984-1_15
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DOI: https://doi.org/10.1007/978-3-7643-7984-1_15
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