11–13 May 2022
Gran Sasso Science Institute
Europe/Rome timezone

Rank-1 ODE for structured eigenvalue optimization

Not scheduled
20m
Gran Sasso Science Institute

Gran Sasso Science Institute

Viale Francesco Crispi 7 67100 L'Aquila (AQ) Italy
Poster Poster

Speaker

Stefano Sicilia (Gran Sasso Science Institute)

Description

A new approach to solve eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to compute structured pseudospectra and their extremal points, and to structured matrix nearness problems such as computing the structured distance to instability. The structure can be a general linear structure and includes, for example, large matrices with a given sparsity pattern, matrices with given range and co-range, and Hamiltonian matrices. Remarkably, the eigenvalue optimization can be performed on the manifold of complex rank-1 matrices, which yields a significant reduction of storage and computational cost. The method relies on a constrained gradient system and the projection of the gradient onto the tangent space of the manifold of complex rank-1 matrices. It is shown that near a local minimizer this projection is very close to the identity map, and so the computationally favorable rank-1 projected system behaves locally like the gradient system.

Primary authors

Prof. Christian Lubich (University of Tubingen) Prof. Nicola Guglielmi (Gran Sasso Science Institute) Stefano Sicilia (Gran Sasso Science Institute)

Presentation materials

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