The Lanczos method (see §4.4) is quite effective
in computing eigenvalues in the ends of the spectrum of if these
eigenvalues are well separated from the remaining spectrum, or
if it is applied to a shifted and inverted matrix operator
, for some reasonable shift
close to the interesting eigenvalues.
If none of these conditions is fulfilled, for instance, if the computation
of a vector
for given
is not feasible with
a direct solver, then variants of the Jacobi-Davidson method [411]
offer an attractive alternative.