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.…
Categoria evento: Seminar on Numerical Analysis
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.…
Applications of AAA Rational Approximation – Lloyd N. Trefethen (Mathematical Institute, University of Oxford)
For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and…
Robust numerical integrators for dynamical low-rank approximation – Gianluca Ceruti (École Polytechnique Fédérale de Lausanne)
The discretization of time-dependent high-dimensional PDEs suffers from an undesired effect, the so-called curse of dimensionality: The amount of data to be stored and treated grows exponentially and exceeds standard capacity of common computational…
Recent extensions of scalar and matrix polynomial properties and their interactions – Aaron Melman (Santa Clara University, USA)
Several results for scalar polynomials are extended and then generalized to matrix polynomials. Among them are a directional version of Pellet’s theorem for both scalarand matrix polynomials, which establishes an exclusion interval for the…