Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix

@article{Guglielmi2011FastAF,
  title={Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix},
  author={Nicola Guglielmi and Michael L. Overton},
  journal={SIAM J. Matrix Analysis Applications},
  year={2011},
  volume={32},
  pages={1166-1192}
}
The ε-pseudospectral abscissa and radius of an n × n matrix are respectively the maximal real part and the maximal modulus of points in its ε-pseudospectrum, defined using the spectral norm. Existing techniques compute these quantities accurately but the cost is multiple singular value decompositions and eigenvalue decompositions of order n, making them impractical when n is large. We present new algorithms based on computing only the spectral abscissa or radius of a sequence of matrices… CONTINUE READING
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