We introduce a new family of geometries on the cone of positive definite matricesobtained from the Hessian of the power potential and provide explicit expressionsfor related quantities such as geodesics and distances.This generalizes in some sense…

# Categoria evento: Seminar on Numerical Analysis

## Caputo and Riemann-Liouville fractional derivatives: a matrix comparison – Mariarosa Mazza (Università dell’Insubria)

Fractional derivatives are a mathematical tool that receivedmuch attention in the last decades because of their non-local behaviorwhich has been demonstrated to be useful when modeling anomalousdiffusion phenomena appearing, e.g., in imaging or…

## Structure-preserving dynamical model order reduction of parametric Hamiltonian systems – Cecilia Pagliantini (TU Eindhoven)

In real-time and many-query simulations of parametric differential equations, computational methods need to face high computational costs to provide sufficiently accurate and stable numerical solutions. To address this issue, model order reduction…

## Computation of generalized matrix functions with rational Krylov methods – Igor Simunec (Scuola Normale Superiore)

Venue: Aula Magna, Dipartimento di Matematica. Generalized matrix functions [3] are an extension of the notion of standard matrix functions to rectangular matrices, defined using the singular value decomposition instead of an eigenvalue…

## Conservative iterative solvers in computational fluid dynamics – Philipp Birken (Lund University)

The governing equations in computational fluid dynamics such as the Navier-Stokes- or Euler equations are conservation laws. Finite volume methods are designed to respect this and the theorem of Lax-Wendroff underscores the importance of it. It…

## Geometric means of quasi-Toeplitz matrices – Jie Meng (University of Pisa)

We study means of geometric type of quasi-Toeplitz matrices, that are semi-infinite matricesA = (a_{i,j}) i,j=1,2,… of the form A = T(a) + E, where E represents a compact operator, and T(a) is a semi-infinite Toeplitz matrix associated with the…

## Compatibility, embedding and regularization of non-local random walks on graphs – Davide Bianchi (University of Insubria, Como, Italy)

Several variants of the graph Laplacian have been introduced to model non-local diffusion pro- cesses, which allow a random walker to “jump” to non-neighborhood nodes, most notably the path graph Laplacians and the fractional graph Laplacian, see…

## (Sparse) Linear Algebra at the Extreme Scales – Fabio Durastante (IAC-CNR)

Sparse linear algebra is essential for a wide variety of scientific applications. The availability of highly parallel sparse solvers and preconditioners lies at the core of pretty much all multi-physics and multi-scale simulations. Technology is…

## A tensor method for semi-supervised learning – Francesco Tudisco (GSSI)

Semi-supervised learning is the problem of finding clusters in a graph or a point-clould dataset where we are given “few” initial input labels. Label Spreading (LS) is a standard technique for this problem, which can be interpreted as a diffusion…

## Efficient iterative methods for the solution of Generalized Lyapunov Equations: Block vs. point Krylov projections, and other controversial decisions – Daniel Szyld (Temple University)

There has been a flurry of activity in recent years in the area of solution of matrix equations. In par- ticular, a good understanding has been reached on how to approach the solution of large scale Lya- punov equations. An effective way to solve…