ml_gdlyap_smith_fac
Nilpotent discrete-time Lyapunov equation solver.
Contents
Syntax
[Z, info] = ml_gdlyap_smith_fac(A, C, E) [Z, info] = ml_gdlyap_smith_fac(A, C, E, opts)
Description
Computes the full-rank solution X = Z'*Z of the generalized discrete-time Lyapunov equation
A'*X*A - E'*X*E = C'*C, (1)
where E is nilpotent, A is invertible, i.e., the matrix pencil s*E - A has only infinite eigenvalues, via the Smith method.
Input
A - matrix with dimensions n x n in (1) C - matrix with dimensions p x n in (1) E - matrix with dimensions n x n in (1) 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
Z - full-rank factor of (1), such that X = Z'*Z 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