Type of Publication: | Journal article |
URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-156534 |
Author: | Schweighofer, Markus |
Year of publication: | 2002 |
Published in: | Journal of Pure and Applied Algebra ; 166 (2002), 3. - pp. 307-319. - ISSN 0022-4049 |
DOI (citable link): | https://dx.doi.org/10.1016/S0022-4049(01)00041-X |
Summary: |
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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Subject (DDC): | 520 Astronomy |
Keywords: | effective Positivstellensatz, strictly positive polynomials |
Link to License: | In Copyright |
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} }
schmuedgen.pdf | 600 |