Archiv der Mathematik

, Volume 89, Issue 5, pp 390–398

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


DOI: 10.1007/s00013-007-2251-y

Cite this article as:
Lasserre, J.B. Arch. Math. (2007) 89: 390. doi:10.1007/s00013-007-2251-y


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).



Real algebraic geometrypositive polynomialssum of squares

Copyright information

©  2007

Authors and Affiliations

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