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The tracial moment problem and trace-optimization of polynomials

Publikationsart Peer-reviewed
Publikationsform Originalbeitrag (peer-reviewed)
Autor/in S. Burgdorf K. Cafuta I. Klep J. Povh,
Projekt Groupes sofiques: algèbre, analyse et dynamique
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Originalbeitrag (peer-reviewed)

Zeitschrift Math. Programming, Ser. A
Titel der Proceedings Math. Programming, Ser. A
DOI 10.1007/s10107-011-0505-8


This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of hermitian squares and commutators decompositions for poly- nomials 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.