Sylvester Equation
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.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,…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.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).