A Unified Approach to Computing Real and Complex Zeros of Zero-dimensional Ideals

@inproceedings{Lasserre2007AUA,
  title={A Unified Approach to Computing Real and Complex Zeros of Zero-dimensional Ideals},
  author={Jean B. Lasserre and Monique Laurent and Philipp Rostalski},
  year={2007}
}
In this paper we propose a unified methodology for computing the set VK(I) of complex (K = C) or real (K = R) roots of an ideal I ⊆ R[x], assuming VK(I) is finite. We show how moment matrices, defined in terms of a given set of generators of the ideal I, can be used to (numerically) find not only the real variety VR(I), as shown in the authors’ previous work, but also the complex variety VC(I), thus leading to a unified treatment of the algebraic and real algebraic problem. In contrast to the… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 21 references

Semidefinite characterization and computation of real radical ideals . To appear in Found

  • M. Laurent J. Lasserre
  • Comp . Math .
  • 2007

and Ágnes Szántó

  • I. Janovitz-Freireich, L. Rónyai
  • Approximate radical of ideals with clusters of…
  • 2006

and D

  • D. Cox, J. Little
  • O’Shea, Ideals, Varieties, and Algorithms: An…
  • 2005

An inverse problem for cubature formulae

  • H. Möller
  • Computat. Technol., 9
  • 2004
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