Archiv der Mathematik

, Volume 89, Issue 5, pp 390–398 | Cite as

Sufficient conditions for a real polynomial to be a sum of squares

Article

Abstract.

We provide explicit sufficient conditions for a polynomial f to be a sum of squares (s.o.s.), linear in the coefficients of f. All conditions are simple and provide an explicit description of a convex polyhedral subcone of the cone of s.o.s. polynomials of degree at most 2d. We also provide a simple condition to ensure that f is s.o.s., possibly after adding a constant.

Mathematics Subject Classification (2000).

12E05 12Y05 

Keywords.

Real algebraic geometry positive polynomials sum of squares 

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Copyright information

©  2007

Authors and Affiliations

  1. 1.LAAS-CNRS and Institute of MathematicsToulouse cedex 4France

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