, Volume 89, Issue 5, pp 390-398

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

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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.

Received: 30 November 2006, Revised: 11 January 2007