Year: 2012
Type: article
Abstract: 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.
DOI: 10.1112/blms/bds007
Author: Daniel Plaumann
Institution: University of Konstanz
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1974817990
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