ml_signm
Matrix sign function iteration.
Contents
Syntax
[Z, info] = ml_signm(A) [Z, info] = ml_signm(A, opts)
Description
The Newton iteration is used to compute the matrix sign function
[ -eye(k) 0 ] Z = sign(A) = T * [ ] * T^(-1), (1) [ 0 eye(n-k) ]
with k eigenvalues of A are in the open left half-plane and n-k are in the open right half-plane.
Input
A - matrix with dimensions n x n from (1) 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
Z - matrix sign function of (1) info - structure, containing the following information:
Entry | 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