technical problems due to the nonlinear dependency of his matrix equations on $\omega$. Most computational methods that deal with nonlinear eigenvalue problems are iterative. They start with an initial guess of the solution and continue with a search scheme in the frequency space. Newton’s method is perhaps the most efficient technique that guarantees a quadratic convergence should the initial guess be close enough to the solution. The key issue in success of any iterative scheme is the attracting or repelling nature of an eigenvalue. It is obvious that only attracting eigenvalues can be captured by iterative methods while we have no priori knowledge of their basins of attraction in order to make our initial guess. The mentioned computational difficulties make it a formidable task to explore all normal modes of a stellar system, which include growing modes as well as stationary van Kampen modes. Moreover, it is not easy to develop a general nonlinear theory based on Kalnajs’s method for studying the interaction of modes.

@P04 [@P05] introduced an alternative method for the normal mode calculation of stellar disks whose outcome was a linear eigenvalue problem for $\omega$. His method is capable of finding all eigenmodes of a stellar disk 