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

@article{Bezerra2010SpectralTA, title={Spectral Transformation Algorithms for Computing Unstable Modes of Large Scale Power Systems}, author={Licio Hernanes Bezerra and Carlos Tomei}, journal={arXiv: Numerical Analysis}, year={2010} }

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…

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