Spectral Transformation Algorithms for Computing Unstable Modes of Large Scale Power Systems

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 Möbius 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 Möbius transforms which together with shift-invert iterat...