TITLE:
On Decompositions of Real Polynomials Using Mathematical Programming Methods
AUTHORS:
Janez Povh
KEYWORDS:
Commutative Polynomial, Noncommutative Polynomial, Sum Of Squares, Semidefinite Programming, Newton Polytope
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.3,
March
24,
2011
ABSTRACT: We present a procedure that gives us an SOS (sum of squares) decomposition of a given real polynomial in variables, if there exists such decomposition. For the case of real polynomials in non-commutative variables we extend this procedure to obtain a sum of hermitian squares SOHS) decomposition whenever there exists any. This extended procedure is the main scientific contribution of the paper.