  In this paper we describe spectral transformation algorithms for the
computation of eigenvalues with positive real part of sparse nonsymmetric
matrix pencils $(J,L)$, where $L$ is of the form $\pmatrix{M&0\cr 0&0}$. For
this we define a different extension of M\"obius transforms to pencils that
inhibits the effect on iterations of the spurious eigenvalue at infinity. These
algorithms use a technique of preconditioning the initial vectors by M\"obius
transforms which together with shift-invert iterations accelerate the
convergence to the desired eigenvalues. Also, we see that M\"obius transforms
can be successfully used in inhibiting the convergence to a known eigenvalue.
Moreover, the procedure has a computational cost similar to power or
shift-invert iterations with M\"obius transforms: neither is more expensive
than the usual shift-invert iterations with pencils. Results from tests with a
concrete transient stability model of an interconnected power system whose
Jacobian matrix has order 3156 are also reported here.
