Computer Science NASC Seminar

Fast Algorithms for Approximating the Pseudospectral Abscissa and Pseudospectral Radius

Nicola Guglielmi, University of L'Aquila

September 17, 2010 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110

Fall 2010 NASC Seminars Calendar


The epsilon-pseudospectral abscissa and radius of an n by n
matrix are respectively the maximum real part and the maximal
modulus of points in its epsilon-pseudospectrum. Existing
techniques compute these quantities accurately but the cost is
multiple singular value decompositions and eigenvalue decompositions
of order n, which makes the methods impractical when n is large.
We present a novel approach based on computing only the spectral
abscissa or radius of a sequence of matrices, generating a monotonic
sequence of lower bounds, and we discuss conditions under which the
sequence of lower bounds converges to a local or global maximizer.
(Joint work with Michael Overton.)

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