`pymor.algorithms.sylvester`¶

Module Contents¶

Solve Sylvester equation by Schur decomposition.

pymor.algorithms.sylvester.solve_sylv_schur(A, Ar, E=None, Er=None, B=None, Br=None, C=None, Cr=None)[source]¶

Solve Sylvester equation by Schur decomposition.

Solves Sylvester equation

\[A V E_r^T + E V A_r^T + B B_r^T = 0\]

or

\[A^T W E_r + E^T W A_r + C^T C_r = 0\]

or both using (generalized) Schur decomposition (Algorithms 3 and 4 in [BKohlerS11]), if the necessary parameters are given.

Parameters

A: Real Operator.
Ar: Real Operator. It is converted into a NumPy array using to_matrix.
E: Real Operator or None (then assumed to be the identity).
Er: Real Operator or None (then assumed to be the identity). It is converted into a NumPy array using to_matrix.
B: Real Operator or None.
Br: Real Operator or None. It is assumed that Br.range.from_numpy is implemented.
C: Real Operator or None.
Cr: Real Operator or None. It is assumed that Cr.source.from_numpy is implemented.

Returns

Raises