ml_disk

Inverse free iteration for the matrix disk function.

Contents

Syntax

[Aspace, Espace, info] = ml_disk(A, E)
[Aspace, Espace, info] = ml_disk(A, E, opts)

Description

Computes the inverse free iteration for the matrix pencil s*E - A with
no eigenvalues on the unit circle. The results can be used to determine
the deflating subspaces of s*E - A corresponding to the eigenvalues
inside and outside the unit circle, respectively.

Input

A    - a matrix with dimensions n x n
E    - a matrix with dimensions n x n
opts - structure, containing the following optional entries:

Parameter
Meaning
AbsTol
nonnegative scalar, tolerance for the absolute change in the last iteration step
default: 0
Info
{0, 1}, used to disable/enable display of verbose status information during iteration steps
default: 0
MaxIter
positive integer, maximum number of iteration steps
default: 100
RelTol
nonnegative scalar, tolerance for the relative change in the last iteration step
default: 1.0e+02*n*eps

Output

Aspace - a matrix with dimensions n x n, the null space of Aspace is
         the deflating subspace corresponding to the eigenvalues
         inside the unit circle
Espace - a matrix with dimensions n x n, the null space of Espace is
         the deflating subspace corresponding to the eigenvalues
         outside the unit circle
info   - structure, containing the following information about the
         inverse free iteration:

Parameter
Meaning
AbsErr
vector, containing the absolute change of the iteration matrix in each iteration step
IterationSteps
number of performed iteration steps
RelErr
vector, containing the relative change of the iteration matrix in each iteration step

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_getqz | ml_signm