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# 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} }

- Published 2011 in SIAM J. Matrix Analysis Applications
DOI:10.1137/100817048

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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