# Numerical Analysis and Scientific Computing Seminar

## Fast Algorithms for Approximating the Pseudospectral Abscissa and Pseudospectral Radius

**Speaker:**
Nicola Guglielmi, University of L'Aquila

**Location:**
Warren Weaver Hall 1302

**Date:**
Sept. 17, 2010, 10 a.m.

**Synopsis:**

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.)