ml_getqz
Subspace extraction method.
Contents
Syntax
[Q, Z, nu] = ml_getqz(A, E, Aspace) [Q, Z, nu] = ml_getqz(A, E, Aspace, [], opts)
[Q, Z, nu] = ml_getqz(A, E, Aspace, Espace) [Q, Z, nu] = ml_getqz(A, E, Aspace, Espace, opts)
Description
Computes orthogonal transformation matrices Q and Z for a deflating subspace of the matrix pencil s*E - A, where the basis is given by the null space of the matrix Aspace. The transformation Q'*(s*E - A)*Z is in block triangular form with the leading block corresponding to the deflating subspace. If additionally the Espace is given, a stabilized version of the algorithm is performed.
Input
- A - a matrix with dimensions n x n
- E - a matrix with dimensions n x n
- Aspace - a matrix with dimensions n x n, with its null space the deflating subspace
- Espace - a matrix with dimensions n x n, complementary subspace of Aspace, is allowed to be empty for the classical subspace extraction method
- opts - structure, containing the following optional entries:
Parameter | Meaning |
Dimension | integer, dimension of the deflating subspace, negative if unknown default: -1 |
RankTol | nonnegative scalar, tolerance multiplied with the largest singular value of Aspace to determine the rank of Aspace, only used if Espace is not given default: log(n)*eps |
Output
- Q - right orthogonal transformation matrix onto the deflating subspace
- Z - left orthogonal transformation matrix onto the deflating subspace
- nu - dimension of the deflating subspace
Reference
P. Benner, Partial stabilization of descriptor systems using spectral projectors, in: P. Van Dooren, S. P. Bhattacharyya, R. H. Chan, V. Olshevsky, A.Routray (Eds.), Numerical Linear Algebra in Signals, Systems and Control, Vol. 80 of Lect. Notes Electr. Eng., Springer Netherlands, 2011, pp. 55--76. https://doi.org/10.1007/978-94-007-0602-6_3
See Also