ml_dsylv_smith_fac

Discrete-time factorized Sylvester equation solver.

Contents

Syntax

[X, info] = ml_dsylv_smith_fac(A, B, G, H)
[X, info] = ml_dsylv_smith_fac(A, B, G, H, [])
[X, info] = ml_dsylv_smith_fac(A, B, G, H, [], [])
[X, info] = ml_dsylv_smith_fac(A, B, G, H, [], [], opts)
[X, info] = ml_dsylv_smith_fac(A, B, G, H, E, F)
[X, info] = ml_dsylv_smith_fac(A, B, G, H, E, F, opts)

Description

Computes the solution matrix of the standard discrete-time factorized Sylvester equation

   A*X*B - X + G*H = 0,                                            (1)

or of the generalized Sylvester equation

   A*X*B - E*X*F + G*H = 0,                                        (2)

using the Smith iteration. It is assumed that the eigenvalues of A and B (or s*E - A and s*F - B) lie inside the open unit disk.

Input

Parameter
Meaning
AbsTol
nonnegative scalar, tolerance for the absolute error in the last iteration step
default: 0
CompTol
nonnegative scalar, tolerance for the row compression during the iteration
default: sqrt(n)*eps
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 error in the last iteration step
default: 1.0e+01*n*eps

Output

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

Reference

P. Benner, Factorized solution of Sylvester equations with applications in control, in: Proc. Intl. Symp. Math. Theory Networks and Syst. MTNS 2004, 2004

See Also

ml_dsylv_smith | ml_sylv_sgn_fac