On Decompositions of Real Polynomials Using Mathematical Programming Methods

Author(s)
Janez Povh

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.

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.

Keywords

Commutative Polynomial, Noncommutative Polynomial, Sum Of Squares, Semidefinite Programming, Newton Polytope

Commutative Polynomial, Noncommutative Polynomial, Sum Of Squares, Semidefinite Programming, Newton Polytope

Cite this paper

nullJ. Povh, "On Decompositions of Real Polynomials Using Mathematical Programming Methods,"*Applied Mathematics*, Vol. 2 No. 3, 2011, pp. 309-314. doi: 10.4236/am.2011.23036.

nullJ. Povh, "On Decompositions of Real Polynomials Using Mathematical Programming Methods,"

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