Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

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Article ID: iaor20132753
Volume: 55
Issue: 1
Start Page Number: 137
End Page Number: 153
Publication Date: May 2013
Journal: Computational Optimization and Applications
Authors: , , ,
Keywords: matrices
Abstract:

This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of Hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of the classical Gram matrix method and the Newton polytope method, which allows us to use semidefinite programming. Throughout the paper several examples are given illustrating the results.

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