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

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  • Kristijan Cafuta

    (Univerza v Ljubljani)

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.

Suggested Citation

  • Kristijan Cafuta, 2019. "Sums of Hermitian squares decomposition of non-commutative polynomials in non-symmetric variables using NCSOStools," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 397-413, June.
    • Handle: RePEc:spr:cejnor:v:27:y:2019:i:2:d:10.1007_s10100-018-0533-z
    DOI: 10.1007/s10100-018-0533-z
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    References listed on IDEAS

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