ml_dlyapdl_smith_fac
Discrete-time dual Lyapunov equation solver.
Contents
Syntax
[R, L, info] = ml_dlyapdl_smith_fac(A, B, C) [R, L, info] = ml_dlyapdl_smith_fac(A, B, C, []) [R, L, info] = ml_dlyapdl_smith_fac(A, B, C, [], opts)
[R, L, info] = ml_dlyapdl_smith_fac(A, B, C, E) [R, L, info] = ml_dlyapdl_smith_fac(A, B, C, E, opts)
Description
Computes the solution matrix of the dual standard discrete-time Lyapunov equations
A*X*A' - X + B*B' = 0, (1) A'*Y*A - Y + C'*C = 0, (2)
or of the dual generalized Lyapunov equations
A*X*A' - E*X*E' + B*B' = 0, (3) A'*Y*A - E'*Y*E + C'*C = 0, (4)
with X = R*R' and Y = L*L' using the Smith iteration. It is assumed that the eigenvalues of A (or s*E - A) lie inside the open unit-circle.
Input
- A - matrix with dimensions n x n in (1), (2) or (3), (4)
- B - matrix with dimensions n x m in (1) or (3)
- C - matrix with dimensions p x n in (2) or (4)
- E - matrix with dimensions n x n in (3), (4), if empty the standard equations (1), (2) are solved
- opts - structure, containing the following optional entries:
Parameter | Meaning |
AbsTol | nonnegative scalar, tolerance for the absolute error in the last iteration step default: 0 |
CompTol | nonnegative scalar, tolerance for the column and row compression during the iteration default: 1.0e-02*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
- X - solution matrix of (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