pymor.algorithms.sylvester

Module Contents

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

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:

• V – Returned if B and Br are given, VectorArray from A.source.

• W – Returned if C and Cr are given, VectorArray from A.source.

Raises:

ValueError – If V and W cannot be returned.