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…
Categoria evento: Seminar on Numerical Analysis
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…
A “matching strategy” for optimal control problems with PDEs as constraints – Santolo Leveque (Scuola Normale Superiore, Pisa)
Saddle-point systems arise quite often in many areas of scientific computing. For instance, this type of system can be found in computational fluid dynamics, constrained optimization, finance, image reconstruction, and many more scientific…
A spectral Galerkin method for the solution of reaction-diffusion equations on metric graphs – Anna Weller (University of Cologne)
We investigate a spectral solution approach for reaction-diffusion equations on graphs interpreted as topological space (metric graphs). Of special interest…
Improved parallel-in-time integration via low-rank updates and interpolation – Stefano Massei (Università di Pisa)
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…
Construction of a sequence of orthogonal rational functions – Raf Vandebril (Department of Computer Science, KU Leuven)
Orthogonal polynomials are an important tool to approximate functions. Orthogonal rational functions provide a powerful alternative if the function of interest is not well approximated by polynomials. Polynomials orthogonal with respect to certain…
Grassmann extrapolation for Born-Oppenheimer Molecular Dynamics – Filippo Lipparini (Dipartimento di Chimica e Chimica Industriale)
Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful, yet very demanding technique in computational quantum chemistry. Performing a BOMD simulation require, for each time step, to compute the energy and forces for a quantum mechanical system,…
Eigenvalue optimization via low-rank ODEs – Nicola Guglielmi (GSSI)
Stability and robustness analysis of linear continuous and discrete dynamical systems is a vast and active interdisciplinary research area. Although the word stability is used in many different contexts, in this talk it is meant to indicate the…
Sampling the eigenvalues of random matrices – Leonardo Robol (University of Pisa)
Random matrices (that is, matrices with random variables as entries) appear in several areas of mathematics and physics. Often, one is interested in sampling their eigenvalues (which are again random variables); we briefly recap the main tools that…