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3.8 Pole/Zero Analysis 317
dae into the matrices A and B. With FrequencyVariable −> Automatic, the symbol is determined
automatically from the status information stored in dae. You can specify the frequency variable
manually with FrequencyVariable −> var.
InitialGuess
With InitialGuess −> {v0, u0}, you can specify initial guesses for the sought eigenvectors v and u.
Both v0 and u0 must be real or complex-valued numeric vectors whose dimensions are compatible
with dae.
MaxIterations
MaxIterations −> n specifies the maximum number of orthogonal correction iterations LREigenpair
should use in order to find an eigenvalue and the corresponding eigenvectors. If LREigenpair fails
to find solutions which satisfy the MaxResidual specification within n iterations, a warning is
generated and the most recent iterates are returned.
MaxResidual
With MaxResidual −> maxres, you can set the convergence criterion for LREigenpair. The value
maxres denotes the maximum L norm the residual vectors r v and r u may have such that the current
set of iterates can be regarded as valid approximations of the sought eigenpairs. LREigenpair stops
iterating as soon as both r v
and r u
fall below maxres.
With the default setting MaxResidual −> Automatic, the maximum residual norm is computed as
maxres ⩵ AccuracyGoal ϑ B A
Note that the value of maxres depends on the setting of the Prescaling option because the norms
of A and B are computed after prescaling.
Prescaling
With Prescaling −> True, LREigenpair scales the rows of the matrix pencil A B such that the
absolute value of the largest coefficient in each row is 1. In general, prescaling improves the numerical
properties of ill-conditioned GEPs and helps to reduce the number of iterations. Prescaling does not
change the eigenvalues and eigenvectors of the matrix pencil. You can turn off prescaling by setting
Prescaling −> False.
ProjectionVectors
Starting with a given initial guess ϑ v u for the sought eigenvalue and eigenvectors, LREigenpair
repeatedly solves the correction equation