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Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Author

Listed:
  • Sabine Burgdorf
  • Kristijan Cafuta
  • Igor Klep
  • Janez Povh

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. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Sabine Burgdorf & Kristijan Cafuta & Igor Klep & Janez Povh, 2013. "Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials," Computational Optimization and Applications, Springer, vol. 55(1), pages 137-153, May.
    • Handle: RePEc:spr:coopap:v:55:y:2013:i:1:p:137-153
    DOI: 10.1007/s10589-012-9513-8
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    References listed on IDEAS

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    1. Halická, M. & de Klerk, E. & Roos, C., 2002. "On the convergence of the central path in semidefinite optimization," Other publications TiSEM 9ca12b89-1208-46aa-8d70-4, Tilburg University, School of Economics and Management.
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