Elenco seminari del ciclo di seminari
“SCUBE”

Series of Semester Seminars organized at the Department of Mathematics, University of Bologna. The presentations mainly cover Numerical Linear Algebra problems and their wide range of applications. Broader contributions are very welcome.
Settembre
12
2025
Catherine Powell
Dimension Reduction Strategies for Computing Stochastic Galerkin Surrogates
nel ciclo di seminari: SCUBE
analisi numerica
Stochastic Galerkin (SG) methods provide a surrogate modelling technique for facilitating forward UQ in PDEs with uncertain inputs. Unlike conventional sampling methods, such as Monte Carlo, SG schemes yield approximations that are functions of the random input variables so that all realisations of the PDE solution are essentially approximated simultaneously. Since they use simple tensor product approximation spaces, standard SG schemes give rise to huge linear systems with coefficient matrices with a characteristic Kronecker product structure. Solving these systems is often a bottleneck when working on standard desktop computers. In this presentation, we will review two potential remedies. The first is to learn a lower-dimensional Galerkin approximation space using a bespoke a posteriori error estimator, leading to smaller linear systems that can be solved with modest computational resources. The second is to retain large tensor product spaces and recast the associated Kronecker system as a matrix equation. One can then apply low rank methods that iteratively construct a bespoke reduced basis and apply projection techniques to solve a problem of reduced size to determine a solution in factored form.
organizzato da: Davide Palitta and Valeria Simoncini
nell'ambito del Progetto R.F.O. 2024 SIMONCINI V del prof. Valeria Simoncini
Maggio
14
2025
Karl Meerbergen, KU Leuven
Rational approximation and linearization of matrix valued functions: algorithms and application
nel ciclo di seminari: SCUBE
analisi numerica
A nonlinear matrix is a matrix whose entries are nonlinear functions of a parameter. Such problems arise from physics (Schroedinger equation) and mechanical engineering (porous materials, boundary element method, e.g.). The last 20 years, rational approximation methods and linearization were proposed to approximate such matrices by linear pencils of much higher dimensions. Applications are the nonlinear eigenvalue problem, parametric linear systems, frequency sweeping, model order reduction and the solution of time dependent problems with nonlinear frequency dependencies. We give an overview of approximation methods with focus on AAA and Krylov methods that exploit the structure of the linear pencil.
organizzato da: Davide Palitta e Valeria Simoncini per la serie di Seminari **Scube**
nell'ambito del Progetto AlmaIdea del prof. Valeria Simoncini
Ottobre
10
2024
Kai Bergermann, Math Dept, TU-Chemnitz, Germany
Numerical linear algebra meets multiplex networks
nell'ambito della serie: SCUBE
nel ciclo di seminari: SCUBE
analisi numerica
Multiplex networks are used to model complex systems from myriad applications. They generalize classical complex networks by recording different types of relationships, different interactions, or changing interactions over time between the same entities in different layers. They possess natural linear algebraic representations in terms of structured matrices, which makes efficient numerical linear algebra techniques a valuable tool for their analysis. In this talk, we give an overview over several network science problems that can be formulated in terms of matrix function expressions, which we approximate by polynomial and rational Krylov methods. We discuss centrality measures, the solution of stiff systems of non-linear differential equations with exponential Runge--Kutta integrators, as well as un- and semi-supervised community detection. Additionally, we present a nonlinear spectral method for core-periphery detection in multiplex networks. All presented methods have a linear runtime scaling, which allows the treatment of large-scale multiplex networks and we present numerical experiments for all considered problems.
organizzato da: Davide Palitta and Valeria Simoncini