Positivity of continuous piecewise polynomials

Details Positivity of continuous piecewise polynomials Positivity of continuous piecewise polynomials

2010-04-19

arxiv.org/abs/1004.3104v3

Mathematics

Optimization and Control

revised version

Scientific paper

Real algebraic geometry provides certificates for the positivity of polynomials on semi-algebraic sets by expressing them as a suitable combination of sums of squares and the defining inequalitites. 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 1-dimensional case, we improve this result to cover all non-negative piecewise polynomials and give explicit degree bounds.

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