Sums of Hermitian squares decomposition of non-commutative polynomials in non-symmetric variables using NCSOStools

Kristijan Cafuta ()
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Kristijan Cafuta: Univerza v Ljubljani

Central European Journal of Operations Research, 2019, vol. 27, issue 2, No 8, 397-413

Abstract: Abstract Numerous applied problems contain matrices as variables, and the formulas therefore involve polynomials in matrices. To handle such polynomials it is necessary study non-commutative polynomials. In this paper we will present an algorithm and its implementation in the free Matlab package NCSOStools using semidefinite programming to check whether a given non-commutative polynomial in non-symmetric variables can be written as a sum of Hermitian squares.

Keywords: Noncommutative polynomial; Sum of Hermitian squares; Semidefinite programming; Matlab toolbox; NCSOStools; 13J30; 90C22; 08B20; 11E25; 90C90 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10100-018-0533-z

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