Seminar in Numerical Analysis: Daniel Kressner (EPFL)

Fast methods for computing pseudospectral quantities

Verifying the stability of a matrix A under perturbations can be a challenging task, especially when additional structure is imposed on the set of admissible perturbations. In the unstructured case, a new class of algorithms has recently been proposed by Guglielmi, Lubich, and Overton to efficiently compute extremal points (such as the right-most point) of the pseudospectrum. In this talk, we discuss two extensions of these algorithms. First, we show how subspace acceleration can be used to significantly speed up convergence, yielding a quadratically convergent subspace method. Second, an extension to certain structured pseudospectra is provided. This gives the possibility to address structures (real Hamiltonian, block diagonal, ...)  that have so far been inaccessible by existing techniques.

This talk is based on joint work with Nicola Guglielmi, Christian Lubich, and Bart Vandereycken.

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