# Generalized Eigenvalue Problem from linear stability analysis

I also posted this in the physics forum, but maybe here it fits better. I am trying to solve a generalized eigenvalue problem raised by linear stability analysis $$AV=\lambda BV.$$ $A$ and $B$ are non-symmetric complex valued matrices. The set of equations I am trying to solve are linearized flow,thermal,solutal fields.(I end up with 3 ODE equations, 4th order for the flow, 2nd order for both thermal and solutal) The system is nondimentionalized, and discretized using 2nd order central finite element method in to $N$ nodes. Then $A$ is the discretized linear operator for my u,T,C, respectively. However, this leads to an order of $N^4$ for some of the terms in $A$, order $N^2$ for $B$. In addition to that, the wave number from the linear stability analysis also introduce some large number to $A$. The order of magnitude of $A$ and $B$ is really different. I am using LAPACK solver (ZGGEV) to solve the problem and the eigenvalues I am getting ranges from +/-$10^6$ to $10^2$. I am wondering if there is a way to scale the problem/eigenvalue such that the information can be interpreted? Any recommendation/thoughts would be really appreciated.

• If your matrices are non symmetric and complex there us no guarantee that your eigenvalues are positive/negative, not even real. If you show your equations you might obtain more help. – nicoguaro May 4 '16 at 17:17