An algorithmic approach to Schmüdgen's Positivstellensatz

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SCHWEIGHOFER, 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

@article{Schweighofer2002algor-15653, title={An algorithmic approach to Schmüdgen's Positivstellensatz}, year={2002}, doi={10.1016/S0022-4049(01)00041-X}, number={3}, volume={166}, issn={0022-4049}, journal={Journal of Pure and Applied Algebra}, pages={307--319}, author={Schweighofer, Markus} }

Schweighofer, Markus 2011-11-10T10:31:19Z 2002 First publ. in: Journal of Pure and Applied Algebra 166 (2002). - S. 307-319 We present a new proof of Schmüdgen's Positivstellensatz concerning the representation of polynomials ƒ ∈ ℝ[X<sub>1</sub>, ...,X<sub>d</sub>] that are strictly positive on a compact basic closed semialgebraic subset S of ℝ<sup>d</sup>. 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 ℝ<sup>d</sup> (minus the origin). Schweighofer, Markus An algorithmic approach to Schmüdgen's Positivstellensatz deposit-license 2011-11-10T10:31:19Z eng

Dateiabrufe seit 01.10.2014 (Informationen über die Zugriffsstatistik)

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