Options.Pairs
Options.Chord
Options.NSigma
Options.FixShift
Options.Track
Options.AvoidStag
If 'yes', then jdqz searches for the complex conjugate eigenpair whenever an eigenpair has been detected. If A and B are real matrices, or the operators correspond to real matrices, then
is an eigenpair if 
is one. Since the eigenpairs are not computed in full
accuracy and since a generalized Schur decomposition
is computed instead of eigenpairs, the conjugate of an
approximate eigenpair may not have the required precision
and jdqz may take additional iterations to obtain
the conjugate pair in the desired accuracy.
To balance the influence of
and 
, the
eigenvalue problem 
and
.
In this formulation, the chordal distance,
and 
than the standard measure 
. Here,
and
.
With Options.Chord = 'yes', jdqz uses the chordal
distance to order the approximate eigenvalues in cases Sigma is specified as a complex or a real number, or as a pair
of complex or real numbers (as target for the desired eigenvalues
or
,
).
Note that, for
, the eigenvalue problems
and
are mathematically equivalent. However, the scaling parameter
affects the chordal distance between
(approximate) eigenvectors. Rescaling may lead to a better balance
between the two operators and . Instead of scaling
the operator , jdqz applies the scaling to intermediate low
dimensional matrices (implicit scaling), which has the same effect, but
may save computational costs.
If 'yes', the jdqz takes as target for the second and following eigenvalues, the best approximate eigenvalues from the current test subspace. Here `best' is taken with respect to Sigma.
Options.FixShift
(default 'no')
If Options.FixShift is scalar and Sigma(1,:) is a scalar, then jdqz takes Sigma as shift in the correction equation until the norm of the residual times Options.FixShift is less than 1. From then on, the shift is taken equal to the present approximate eigenvalue.
Options.Track
(default '1e-4')
If the wanted eigenvalue is relatively far from the target, then the algorithm may select approximate eigenvalues that are accidentally close to the target instead of the approximate eigenvalue that is close to the wanted eigenvalue. To avoid this type of misselection, the target can be moved to an approximate eigenvalue that is close to the wanted eigenvalue. The size of the norm of the residual is used to measure the quality of the approximate eigenvalue. If norm(r)<= Options.track, then the associated approximate eigenvalue is used as target in the next iteration step.
Options.AvoidStag (default 'no')
In some situations, the algorithm stagnates because the computed expansion vector for the search subspace belongs to the search subspace or is close to it. With 'yes', jdqz tries to remedy this type of stagnation. In the correction equation in the next iteration step, jdqz projects then on the complete search subspace rather than on the current eigenvector approximation.