Due Giorni di Algebra Lineare Numerica e Applicazioni

Session

Morning Session III

21 Jan 2025, 09:00

Building E (Aula Magna "Fratelli Pontecorvo", Building E, Polo Fibonacci. Pisa)

Description

Chair: Marco Donatelli

5. Modelling advection on distance-weighted directed networks

Francesco Zigliotto (Scuola Normale di Pisa)

21/01/2025, 09:00

Talk

We introduce a mathematical model to capture and describe the dynamics of the advection differential equation on distance-weighted directed graphs, with applications to various networked systems. The primary objective of our model is to generalize advection processes—which traditionally describe phenomena like fluid flow or traffic movement—by formulating them within the framework of discrete...

46. Explicit Characterization of Consensus in a Distributed Estimation Problem on Chain Graphs

Prof. Cristiano Maria Verrelli (University of Rome Tor Vergata, Electronic Engineering Department)

21/01/2025, 09:20

Talk

This Abstract briefly describes the original results that are to be submitted to the international journal IEEE Transactions on Automatic Control. In particular, the problem of looking for time-varying vectors ${\hat{\Theta}}(t)$ - named $\Theta$-estimates - which exponentially converge to the unknown constant parameter vector $\Theta \in \mathbb{R}^{m}$ defined by the set of linear...

33. Walk-induced strategies for updating Katz centrality in simple graphs

Alessandro Filippo (University of Rome Tor Vergata)

21/01/2025, 09:40

Talk

Katz centrality is one of the most widely used indices in network science to determine the relative influence of a node within a network. Its unique feature is that it can be expressed as the solution of the (typically sparse) linear system $(I- \alpha A) \mathbf{x} = \mathbf{1}$, where $A$ is the adjacency matrix of the underlying graph and $\alpha>0$ is a dumping parameter such that $\alpha...

12. Generalized approximating class of sequences and asymptotic block structures with rectangular Toeplitz blocks.

Alec Jacopo Almo Schiavoni Piazza (SISSA)

21/01/2025, 10:00

Talk

In the talk, the problem of identifying the distribution in the Weyl sense (singular values and eigenvalues) is treated, when block matrix-sequences with rectangular Toeplitz blocks are considered. The case of sequences whose block sizes tend to rational numbers is of more classical flavour and is concisely introduced.
Using recent results regarding the notion of generalized approximating...

26. Eigenvalues and singular values of variable Toeplitz matrices and matrix-sequences, with application to variable two-step BDF approximations to parabolic equations

NIKOS BARAKITIS (University of Insubria)

21/01/2025, 10:20

Talk

In the present talk we consider a general class of varying Toeplitz matrix sequences and we prove that they belong to the maximal *-algebra of GLT matrix sequences. We then examine specific structures within the class stemming from variable two-step backward difference formulae (BDF) approximations of parabolic equations as treated in previous works for studying the stability.

For both the...

3. SVD-based Line Integral Methods for preserving multiple invariants of Hamiltonian problems

Dr Gianmarco Gurioli (University of Florence)

Talk

In this talk, we generalize the class of energy-conserving Runge-Kutta methods, named Hamiltonian Boundary Value Methods, to handle the numerical solution of Hamiltonian problems with additional independent invariants besides the Hamiltonian. The proposed strategy relies on the solution of a perturbed problem, where a minimum norm perturbation is computed by resorting to the singular value...