In this paper we present algorithms and their implementations in the computational algorithms package NCSOStools for extraction of the global eigenvalue optimizers and extraction of eigenvalue ...optimizers over the free ball. They are based on free noncommutative analogs of classical Gram matrix method, which allows us to use semidefinite programming, solution to a truncated free noncommutative moment problem via flat extensions and the Gelfand-Naimark-Segal (GNS) construction.
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