MATH Seminar

Title: Approximating Stability Radii
Seminar: Numerical Analysis and Scientific Computing
Speaker: Manuela Manetta of School of Mathematics Georgia Institute of Technology
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2014-12-05 at 12:00PM
Venue: MSC W301
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Abstract: The distance of a n × n stable matrix to the set of unstable matrices, the so-called distance to instability, is a well-known measure of linear dynamical system stability. Existing techniques compute this quantity accurately but the cost is of the order of multiple SVDs of order n, which makes the method suitable for medium-size problems. A new approach is presented, based on Newton’s iteration applied to the pseudospectral abscissa, whose implementation is obtained by discretization of differential equations for low-rank matrices, and is particularly suited for large sparse matrices.