An algorithmic approach to Schmüdgen's Positivstellensatz

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2002
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Journal of Pure and Applied Algebra ; 166 (2002), 3. - pp. 307-319. - ISSN 0022-4049
Abstract
We present a new proof of Schmüdgen's Positivstellensatz concerning the representation of polynomials ƒ ∈ ℝ[X1, ...,Xd] that are strictly positive on a compact basic closed semialgebraic subset S of ℝd. Like the two other existing proofs due to Schmüdgen and Wörmann, our proof also applies the classical Positivstellensatz to non-constructively produce an algebraic evidence for the compactness of S. But in sharp contrast to Schmüdgen and Wörmann we explicitly construct the desired representation of ƒ from this evidence. Thereby we make essential use of a theorem of Pólya concerning the representation of homogeneous polynomials that are strictly positive on an orthant of ℝd (minus the origin).
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520 Astronomy
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effective Positivstellensatz,strictly positive polynomials
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ISO 690SCHWEIGHOFER, Markus, 2002. An algorithmic approach to Schmüdgen's Positivstellensatz. In: Journal of Pure and Applied Algebra. 166(3), pp. 307-319. ISSN 0022-4049. Available under: doi: 10.1016/S0022-4049(01)00041-X
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@article{Schweighofer2002algor-15653,
  year={2002},
  doi={10.1016/S0022-4049(01)00041-X},
  title={An algorithmic approach to Schmüdgen's Positivstellensatz},
  number={3},
  volume={166},
  issn={0022-4049},
  journal={Journal of Pure and Applied Algebra},
  pages={307--319},
  author={Schweighofer, Markus}
}
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