Pseudospectra and utmost right norm
My research internship was about the asymptotic stability of linear system when the data is perturbed, using pseudospectra.
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During my research internship at the Chair of Numerical Algorithms and High-Performance Computing, I studied the asymptotic stability of linear dynamical systems, focusing on methods that go beyond the classical eigenvalue approach. In particular, I examined the use of the utmost right norm to assess the long-term behavior of trajectories, and the links with pseudospectra, which give a more reliable picture of stability under perturbations than eigenvalues alone. To improve the algorithm used to trace pseudospectra, I was introduced to randomization techniques, which make it possible to approximate and test stability properties more efficiently, without the need to project onto matrix manifolds. This internship really was an enriching experience that enabled me to gain more knowledge on a field that I'd yet to discover, and I am grateful for Laidlaw program for having given me this opportunity to discover the world of research in mathematics.
Béatrice Serrurier
(She/Her)
Student, EPFL
