ml_gdlyapdl_smith_fac
Nilpot. discrete-time dual Lyapunov equation solver.
Contents
Syntax
[R, L, info] = ml_gdlyapdl_smith_fac(A, B, C, E) [R, L, info] = ml_gdlyapdl_smith_fac(A, B, C, E, opts)
Description
Computes the full-rank solutions X = R*R' and Y = L*L' of the generalized discrete-time dual Lyapunov equations
E*X*E' - A*X*A' + B*B' = 0, (1) E'*Y*E - A'*Y*A + C'*C = 0, (2)
where E is nilpotent and A is invertible, i.e., the matrix pencil s*E - A has only infinite eigenvalues, via the Smith iteration.
Input
- A - matrix with dimensions n x n in (1) and (2)
- B - matrix with dimensions n x m in (1)
- C - matrix with dimensions p x n in (2)
- E - matrix with dimensions n x n in (1) and (2)
- opts - structure, containing the following optional entries:
Parameter | Meaning |
AbsTol | nonnegative scalar, tolerance for the absolute gain in the last iteration step default: 0 |
Index | nonnegative integer, index of nilpotency of the matrix E used to set the exact number of iteration steps, if the index is unknown Inf is set default: Inf |
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 gain in the last iteration step default: 1.0e+01*n*eps |
Output
- R - full-rank factor of (1), such that X = R*R'
- L - full-rank factor of (2), such that Y = L*L'
- 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
T. Stykel, Low-rank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal. 30 (2008) 187--202.
See Also