Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Burgdorf, SabineCafuta, KristijanKlep, IgorPovh, Janez2013-10-012013-10-012013-10-01201310.1007/s10589-012-9513-8https://infoscience.epfl.ch/handle/20.500.14299/95468WOS:000317468600006This 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.Sum of squaresSemidefinite programmingNoncommutative polynomialMatlab toolboxNewton polytopeFree positivityAlgorithmic aspects of sums of Hermitian squares of noncommutative polynomialstext::journal::journal article::research article