High Quality Content by WIKIPEDIA articles!In control theory, the Sylvester equation is the matrix equation of the formUsing the Kronecker product notation and the vectorization operator operatorname{vec}, we can rewrite the equation in the formA classical algorithm for the numerical solution of the Sylvester equation is the Bartels--Stewart algorithm, which consists in transforming A and B into Schur form by a QR algorithm, and then solving the resulting triangular system via back-substitution. This algorithm, whose computational cost is O(n3) arithmetical operations, is used, among others, by LAPACK, Matlab and GNU Octave (in the lyap function).

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