  Generalized eigenvalue problems involving a singular pencil may be very
challenging to solve, both with respect to accuracy and efficiency. While Part
I presented a rank-completing addition to a singular pencil, we now develop two
alternative methods. The first technique is based on a projection onto
subspaces with dimension equal to the normal rank of the pencil while the
second approach exploits an augmented matrix pencil. The projection approach
seems to be the most attractive version for generic singular pencils because of
its efficiency, while the augmented pencil approach may be suitable for
applications where a linear system with the augmented pencil can be solved
efficiently.
