Fast algorithms for the computation of the pseudospectral abscissa and pseudospectral radius.

Applied and Computational Mathematics Seminar
Monday, November 9, 2009 - 13:00
1 hour (actually 50 minutes)
Skiles 255
Università di L'Aquila
This is a joint work with Michael Overton (Courant Institute, NYU). The epsilon-pseudospectral abscissa and radius of an n x 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 SVDs of order n, which makesthe method suitable to middle size problems. We present a novel approach based on computing only the spectral abscissa or radius or a sequence of matrices, generating a monotonic sequence of lower bounds which, in many but not all cases, converges to the pseudospectral abscissa or radius.