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

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

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

ml_gdlyap_smith_fac | ml_lyap_sgn_fac