  An numerical iterative framework for global modal stability analysis of
compressible flows using a parallel environment is presented. The framework
uses a matrix-free implementation to allow computations of large scale
problems. Various methods are tested with regard to convergence acceleration of
the framework. The methods consist of a spectral Cayley transformation used to
select desired Eigenvalues from a large spectrum, an improved linear solver and
a parallel block-Jacobi preconditioning scheme.
