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