An algorithmic approach to Schmüdgen's Positivstellensatz

Schweighofer, Markus

An algorithmic approach to Schmüdgen's Positivstellensatz

Dateien

schmuedgen.pdfGröße: 995.54 KBDownloads: 525

Datum

2002

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Journal of Pure and Applied Algebra. 2002, 166(3), pp. 307-319. ISSN 0022-4049. Available under: doi: 10.1016/S0022-4049(01)00041-X

Zusammenfassung

We present a new proof of Schmüdgen's Positivstellensatz concerning the representation of polynomials ƒ ∈ ℝ[X₁, ...,X_d] that are strictly positive on a compact basic closed semialgebraic subset S of ℝ^d. 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^d (minus the origin).

Fachgebiet (DDC)

520 Astronomie

Schlagwörter

effective Positivstellensatz, strictly positive polynomials

Zitieren

ISO 690

SCHWEIGHOFER, Markus, 2002. An algorithmic approach to Schmüdgen's Positivstellensatz. In: Journal of Pure and Applied Algebra. 2002, 166(3), pp. 307-319. ISSN 0022-4049. Available under: doi: 10.1016/S0022-4049(01)00041-X

BibTex

@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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