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Positivity of continuous piecewise polynomials

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2012

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https://doi.org/10.1112/blms/bds007
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http://arxiv.org/abs/1004.3104v3

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Bulletin of the London Mathematical Society. Wiley. 2012, 44(4), pp. 749-757. ISSN 0024-6093. eISSN 1469-2120. Available under: doi: 10.1112/blms/bds007

Zusammenfassung

Real algebraic geometry provides certificates for the positivity of polynomials on semialgebraic sets by expressing them as a suitable combination of sums of squares and the defining inequalities. We show how Putinar's theorem for strictly positive polynomials on compact sets can be applied in the case of strictly positive piecewise polynomials on a simplicial complex. In the one‐dimensional case, we improve this result to cover all non‐negative piecewise polynomials and give explicit degree bounds.

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510 Mathematik

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ISO 690PLAUMANN, Daniel, 2012. Positivity of continuous piecewise polynomials. In: Bulletin of the London Mathematical Society. Wiley. 2012, 44(4), pp. 749-757. ISSN 0024-6093. eISSN 1469-2120. Available under: doi: 10.1112/blms/bds007
BibTex
@article{Plaumann2012Posit-48959,
  year={2012},
  doi={10.1112/blms/bds007},
  title={Positivity of continuous piecewise polynomials},
  number={4},
  volume={44},
  issn={0024-6093},
  journal={Bulletin of the London Mathematical Society},
  pages={749--757},
  author={Plaumann, Daniel}
}
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