ml_dsylv_smith
Discrete-time Sylvester equation solver.
Contents
Syntax
[X, info] = ml_dsylv_smith(A, B, C) [X, info] = ml_dsylv_smith(A, B, C, []) [X, info] = ml_dsylv_smith(A, B, C, [], []) [X, info] = ml_dsylv_smith(A, B, C, [], [], opts)
[X, info] = ml_dsylv_smith(A, B, C, E, F) [X, info] = ml_dsylv_smith(A, B, C, E, F, opts)
Description
Computes the solution matrix of the standard discrete-time Sylvester equation
A*X*B - X + C = 0, (1)
or of the generalized Sylvester equation
A*X*B - E*X*F + C = 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
- 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 n x n from (2), if empty it is assumed to be the identity
- F - matrix with dimensions m x m 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
V. Simoncini, Computational methods for linear matrix equations, SIAM Rev. 38 (3) (2016) 377--441. https://doi.org/10.1137/130912839
See Also