The signature of a quadratic form plays an important role in the study
of quadratic forms in a Witt group. For any algebraic variety X over the
real numbers R, it allows one to relate quadratic forms over X to the
singular
cohomology of the real points X(R). This has applications to bounding the
order of torsion in the Witt group of quadratic forms over X.

Fri

12/05/2014

(in 12 days)

12:00pm

Seminar: Numerical Analysis and Scientific Computing

Approximating Stability Radii

Manuela Manetta, School of Mathematics Georgia Institute of Technology

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.