Speaker: Nicola Guglielmi
Affiliation: Gran Sasso Science Institute
Venue: Aula Volterra, Scuola Normale Superiore

Remark. Il seminario si terrà in presenza. Chi fosse interessato a
partecipare deve scrivere a classi@sns.it  entro le 9:00 di Lunedì
7 marzo 2022

Abstract. Stability and robustness analysis of linear continuous
and discrete dynamical systems is a vast and active interdisciplinary
research area.   
Although the word stability is used in many different contexts, in this
talk it is meant to indicate the broad spectrum of issues that arise in
the analytical and numerical study of dynamical and control systems,
especially in relation to qualitative  information of the system under
study.  

These issues result from the need to develop stable and reliable systems
robustly  preserving essential qualitative properties.

The analysis of these features is often based on eigenvalue optimization
or on pseudospectral measures of a certain matrix A, where the
structure of A (e.g., sparse, Hamiltonian, nonnegative, Toeplitz, etc.) plays
an important role.

The main goal of this talk is to show how these structured distances can
be approximated.
The proposed method is a two-level iterative algorithm, where in an inner
iteration a gradient flow drives perturbations to the original matrix of a
fixed size into a minimum of a functional that depends on eigenvalues
(and possibly eigenvectors), and in an outer iteration the perturbation size
is optimized such that the functional reaches some target value (for
example O).

An interesting point - related to certain low-rank properties of extremizers
- lies in the possibility of considering gradient flows on low-rank manifolds.

The talk is mainly inspired by joint works with Christian Lubich (Tuebingen).

Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4