ml_sylv_sgn
Continuous-time Sylvester equation solver.
Contents
Syntax
[X, info] = ml_sylv_sgn(A, B, C) [X, info] = ml_sylv_sgn(A, B, C, []) [X, info] = ml_sylv_sgn(A, B, C, [], []) [X, info] = ml_sylv_sgn(A, B, C, [], [], opts)
[X, info] = ml_sylv_sgn(A, B, C, E, F) [X, info] = ml_sylv_sgn(A, B, C, E, F, opts)
Description
Computes the solution matrix of the standard Sylvester equation
AX + XB = C, (1)
or of the generalized Sylvester equation
A*X*E + F*X*B = C, (2)
using the sign function iteration. It is assumed that the eigenvalues of A and B (or s*F - A and s*E - B) lie in the open left half-plane.
Input
A - matrix with dimensions n x n from (1) or (2) B - matrix with dimensions m x m from (1) or (2) C - matrix with dimensions n x m from (1) or (2) E - matrix with dimensions m x m from (2), if empty it is assumed to be the identity F - matrix with dimensions n x n from (2), if empty it is assumed to be the identity opts - structure, containing the following optional entries:
Parameter | Meaning |
AbsTol | nonnegative scalar, tolerance for the absolute error 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 error in the last iteration step default: 1.0e+01*n*eps |
Output
X - solution of the Sylvester equation (1) or (2) info - structure, containing the following information:
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