NCSOStools

NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials. NCSOStools is a Matlab toolbox for symbolic computation with polynomials in noncommuting (NC) variables; constructing and solving sum of Hermitian squares (with commutators) programs for polynomials in NC variables. It can be used in combination with semidefinite programming software, such as SeDuMi, SDPA or SDPT3, to solve these constructed programs. This paper provides an overview of the theoretical underpinning of the sum of Hermitian squares (with commutators) programs and provides a gentle introduction to the primary features of NCSOStools


References in zbMATH (referenced in 14 articles , 1 standard article )

Showing results 1 to 14 of 14.
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  1. Burgdorf, Sabine; Klep, Igor; Povh, Janez: Optimization of polynomials in non-commuting variables (2016)
  2. Klep, Igor; Povh, Janez: Constrained trace-optimization of polynomials in freely noncommuting variables (2016)
  3. Cafuta, Kristijan; Klep, Igor; Povh, Janez: Rational sums of Hermitian squares of free noncommutative polynomials (2015)
  4. Wittek, Peter: Algorithm 950: Ncpol2sdpa -- sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables (2015)
  5. Cimprič, Jakob; Helton, J.William; Klep, Igor; McCullough, Scott; Nelson, Christopher: On real one-sided ideals in a free algebra (2014)
  6. Helton, J.William; Klep, Igor; Nelson, Christopher S.: Noncommutative polynomials nonnegative on a variety intersect a convex set (2014)
  7. Blekherman, Grigoriy (ed.); Parrilo, Pablo A. (ed.); Thomas, Rekha R. (ed.): Semidefinite optimization and convex algebraic geometry (2013)
  8. Burgdorf, Sabine; Cafuta, Kristijan; Klep, Igor; Povh, Janez: Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials (2013)
  9. Burgdorf, Sabine; Cafuta, Kristijan; Klep, Igor; Povh, Janez: The tracial moment problem and trace-optimization of polynomials (2013)
  10. Cafuta, Kristijan; Klep, Igor; Povh, Janez: Optimizations of free polynomials (2013)
  11. Helton, J.William; Klep, Igor; McCullough, Scott: The convex Positivstellensatz in a free algebra (2012)
  12. Cafuta, Kristijan; Klep, Igor; Povh, Janez: NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials (2011)
  13. Klep, Igor; Povh, Janez: Semidefinite programming and sums of Hermitian squares of noncommutative polynomials (2010)
  14. Pironio, S.; Navascués, M.; Acín, A.: Convergent relaxations of polynomial optimization problems with noncommuting variables (2010)