#### Conference abstracts

Session B7 - Numerical Linear Algebra

July 15, 15:00 ~ 15:30 - Room B5

## Subspace methods for computing the Crawford number and the real pseudospectral abscissa

### Bart Vandereycken

### University of Geneva, Switzerland, Switzerland - bart.vandereycken@unige.ch

Certain eigenvalue or singular value optimization algorithms require repeatedly calculating the spectrum of a smoothly varying matrix. Two examples are the computation of the Crawford number and the real pseudospectral abscissa. In this talk, I will show how the computed eigenvectors and singular vectors can be used to construct subspace methods that approximate the original problems increasingly well. For the Crawford number, the subspace method is equivalent to one in [Kangal et al., A Subspace Method for Large Scale Eigenvalue Optimization, 2017] but our new convergence analysis predicts the numerical order of convergence very well. For the real pseudospectral abscissa, our algorithm is new and we prove its superlinear convergence.

Joint work with Ding Lu (University of Geneva, Switzerland) and Daniel Kressner (EPF Lausanne, Switzerland).