Per oltre un secolo, i matematici sono stati affascinati dallo studio delle proprietà di famiglie di matrici. Gli oggetti con…
Categoria evento: Seminar on Numerical Analysis
Calcolo della traccia di funzioni di matrici mediante stimatori stocastici e probing – Michele Rinelli (Scuola Normale Superiore)
Le funzioni di matrici [1] sono un potente strumento dell’algebra lineare numerica per l’analisi di vari problemi provenienti dalle applicazioni.…
Caratterizzazione strutturale dell’acqua liquida: un approccio computazionale basato sulla teoria dei grafi (Pisan Young Seminars in Applied and NUmerical Mathematics) – Chiara Faccio (Scuola Normale Superiore)
L’acqua liquida, oltre ad essere fondamentale per la vita sulla Terra, ha da lungo tempo affascinato gli scienziati a causa…
On the influence of stochastic rounding bias in implementing gradient descent with applications in low-precision training – Lu Xia (Eindhoven University of Technology)
In the context of low-precision computation for the training of neural networks with thegradient descent method (GD), the occurrence of deterministic rounding errors often leadsto stagnation or adversely affects the convergence of the optimizers.…
A Tensor Gradient Cross for Hamilton-Jacobi-Bellman equations – Luca Saluzzi (Scuola Normale Superiore, Pisa)
Hamilton-Jacobi-Bellman (HJB) equation plays a central role in optimal control and differential games, enabling the computation of robust controls in feedback form. The main disadvantage for this approach depends on the so-called curse of…
Stochastic probing methods for estimating the trace of functions of sparse symmetric matrices – Michele Rinelli (Scuola Normale Superiore)
We consider the combination of two approaches for the trace estimation of a symmetric matrix function f(A) when the only feasible operations are matrix-vector products and quadratic forms with f(A): stochastic estimators, such as the Hutchinson…
Grassmann extrapolation of density matrices as a tool to accelerate Born-Oppenheimer molecular dynamics – Federica Pes (Università di Pisa)
Born-Oppenheimer molecular dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory (DFT) BOMD calculation is the solution to the DFT nonlinear equations that requires an iterative procedure that…
Perfect Shifted QR for Rank Structured Pencils – Vandebril Raf (KU Leuven)
It is known that executing a perfect shifted QR step via the implicit QR algorithm performs poor in terms of stability, and accuracy. Typically several steps are required before deflation actually takes place. This behavior can be remedied by…
Model order reduction of parametric Hamiltonian systems on matrix manifolds – Cecilia Pagliantini (University of Pisa)
Model order reduction of parametric differential equations aims at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. The development of reduced order models for Hamiltonian…
COLLOQUIO DE GIORGI – Dirac and Lagrange structures in energy-based mathematical modeling – Volker Mehrmann (Technische Universität Berlin)
Most real world dynamical systems consist of subsystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, and algebraic equations, combined with input and output connections.…