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

ml_disk | ml_getqz