An algorithmic approach to Schmüdgen's Positivstellensatz

Schweighofer, Markus

doi:10.1016/S0022-4049(01)00041-X

An algorithmic approach to Schmüdgen's Positivstellensatz

Publikationstyp:	Zeitschriftenartikel
URI (zitierfähiger Link):	http://nbn-resolving.de/urn:nbn:de:bsz:352-156534
Autor/innen:	Schweighofer, Markus
Erscheinungsjahr:	2002
Erschienen in:	Journal of Pure and Applied Algebra ; 166 (2002), 3. - S. 307-319. - ISSN 0022-4049
DOI (zitierfähiger Link):	https://dx.doi.org/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
Link zur Lizenz:	Nutzungsbedingungen

Zitieren

Dateien zu dieser Ressource

Name: schmuedgen.pdf

Größe: 995.5Kb

Format: PDF

Öffnen

Prüfsumme: MD5:4980bbdbb7b41ea69293afa9d21151ea

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 terms-of-use 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[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). Schweighofer, Markus An algorithmic approach to Schmüdgen's Positivstellensatz 2011-11-10T10:31:19Z eng