scipy.linalg.solve_sylvester¶
- scipy.linalg.solve_sylvester(a, b, q)[source]¶
Computes a solution (X) to the Sylvester equation (AX + XB = Q).
New in version 0.11.0.
Parameters: a : (M, M) array_like
Leading matrix of the Sylvester equation
b : (N, N) array_like
Trailing matrix of the Sylvester equation
q : (M, N) array_like
Right-hand side
Returns: x : (M, N) ndarray
The solution to the Sylvester equation.
Raises: LinAlgError
If solution was not found
Notes
Computes a solution to the Sylvester matrix equation via the Bartels- Stewart algorithm. The A and B matrices first undergo Schur decompositions. The resulting matrices are used to construct an alternative Sylvester equation (RY + YS^T = F) where the R and S matrices are in quasi-triangular form (or, when R, S or F are complex, triangular form). The simplified equation is then solved using *TRSYL from LAPACK directly.