Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Authors:
Sabine Burgdorf;Kristijan Cafuta;Igor Klep;Janez Povh
Affiliations:
SB-MATHGEOM-EGG, EPFL, Lausanne, Switzerland 1015;Fakulteta za elektrotehniko, Laboratorij za uporabno matematiko, Univerza v Ljubljani, Ljubljana, Slovenia 1000;Department of Mathematics, The University of Auckland, Auckland, New Zealand 1142;Fakulteta za informacijske študije v Novem mestu, Novo mesto, Slovenia 8000
Venue:
Computational Optimization and Applications
Year:
2013

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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.