Scientific Computing and Matrix Computations Seminar: Subspace methods for computing real pseudospectral abscissa and eigenvalue optimization

Seminar: EE: CS | April 3 | 2-3 p.m. | 380 Soda Hall

 Ding Lu, UC Davis

 Electrical Engineering and Computer Sciences (EECS)

Applications in computational science and engineering often involve
optimizations that require repeatedly calculating the spectrum of a smoothly
varying matrix valued function. In this talk, we consider one such a problem
for computing the real $\epsilon$-pseudospectral abscissa of a real matrix
$A$, namely, the largest real part of the eigenvalues of all real matrices
that are $\epsilon$-close to $A$. We present a subspace method to build
subspace surrogates that can approximate the exact solution with a locally
superlinear rate of convergence. The subspace method can also be applied to
the problem of univariate eigenvalue optimization of Hermitian matrices. There
we can show that the order of convergence is $1+\sqrt{2}$. Applications for
coercivity constant estimation of boundary integral operators in acoustic
scattering will be discussed., 5106489542