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3.8 Pole/Zero Analysis 325
Note that you may also change the option settings of the selected GEP solver directly with
SetOptions[gepsolver, opts]. However, with GEPSolverOptions, you can specify private option
settings which will only be used in conjunction with ApproximateDeterminant.
InitialSolution
With InitialSolution −> initsol, you can specify the initial reference solution for the GEP to be
approximated. The value of InitialSolution must be given in the same format as the return value
of LREigenpair (Section 3.8.7). Possible values are:
Automatic
{lambda , v , u , † † † }
compute the initial reference solution using the GEP solver
specified with GEPSolver
use the given initial reference solution
Values for the InitialSolution option.
MaxDivergentSteps
MaxDivergentSteps −> n specifies the maximum number of divergent iterations allowed in the
error tracking step following the elimination of a matrix entry. Iterates are considered divergent if
the residual of the numerical solution of the GEP becomes larger between two consecutive steps.
If the number of divergent steps exceeds the specified maximum in the error tracking process,
ApproximateDeterminant aborts the iterations, reinserts the current term into the matrix, and
continues with the next term.
MaxIterations
MaxIterations −> n specifies the maximum number of error tracking iterations performed after
removing a matrix entry. An approximation is considered valid if the iterations converge within
n steps, and if both the MaxResidual and MinMAC specifications are satisfied. See also LREigenpair
(Section 3.8.7).
If you set GEPSolver −> LREigenpair, note that the MaxIterations setting given for
ApproximateDeterminant is not passed to LREigenpair. To specify the maximum number
of iterations for the GEP solver, change the value of GEPSolverOptions.
MaxResidual
MaxResidual −> posreal specifies the convergence criterion for the error tracking iterations.
MaxResidual is one of the key options you should play with in order to obtain good results from
ApproximateDeterminant. You should choose the value as large as possible to allow for a reasonable