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

ml_disk | ml_signm