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Meer, Klaus ; Malajovich, Gregorio

On the Complexity of Computing Multi-Homogeneous Bézout Numbers

04401.MeerKlaus.Paper.146.pdf (0.3 MB)


We study the question how difficult it is to compute the multi-homogeneous B\'ezout number for a polynomial system of given number $n$ of variables and given support $A$ of monomials with non-zero coefficients. We show that this number is NP-hard to compute. It cannot even be efficiently approximated within an arbitrary, fixed factor unless P = NP. This is joint work with Gregorio Malajovich.

BibTeX - Entry

  author =	{Klaus Meer and Gregorio Malajovich},
  title =	{On the Complexity of Computing Multi-Homogeneous B{\'e}zout Numbers},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  year =	{2005},
  editor =	{Thomas M{\"u}ller-Gronbach and Erich Novak and Knut Petras and Joseph F. Traub},
  number =	{04401},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: multi-homogeneous B{\'e}zout numbers , number of roots of polynomials , approximation algorithms}

Keywords: multi-homogeneous Bézout numbers , number of roots of polynomials , approximation algorithms
Seminar: 04401 - Algorithms and Complexity for Continuous Problems
Issue Date: 2005
Date of publication: 19.04.2005

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