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

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

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