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[Indico] Prof. Vandebril Raf, Perfect Shifted QR for Rank Structured Pencils, 13/04/2023, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 11 Apr '23

11 Apr '23

Title: Perfect Shifted QR for Rank Structured Pencils, Speaker(s): Prof. Vandebril Raf, KU Leuven, Date and time: 13 Apr 2023, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/182 Abstract -------- 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 determining the similarity transformation via the associated eigenvector. Similar techniques can be deduced for the QZ algorithm and the rational QZ algorithm. In this talk we generalize this even further and present an approach for executing a perfect shifted QR step for general rank structured pencils. We prove that the rank structures of the matrices involved in the pencil are preserved, and moreover we examine the preservation of spectral properties of subblocks in the pencil.Authors: Nicola Mastronardi, Marc Van Barel, Raf Vandebril, and Paul Van Dooren -- Indico :: Email Notifier https://events.dm.unipi.it/e/182

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[Indico] Cecilia Pagliantini, Model order reduction of parametric Hamiltonian systems on matrix manifolds, 28/03/2023, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 27 Mar '23

27 Mar '23

Title: Model order reduction of parametric Hamiltonian systems on matrix manifolds, Speaker(s): Cecilia Pagliantini, University of Pisa, Date and time: 28 Mar 2023, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/176 Abstract -------- 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 systems is challenged by several factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the slowly decaying Kolmogorov n-width of transport-dominated and non-dissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations; and (iii) nonlinear operators require hyper-reduction techniques that preserve the gradient structure of the flow velocity.We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to adapt in time an approximate low-dimensional phase space endowed with the geometric structure of the full model and to ensure that the reduced flow is still Hamiltonian. -- Indico :: Email Notifier https://events.dm.unipi.it/e/176

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[Indico] Cecilia Pagliantini, Model order reduction of parametric Hamiltonian systems on matrix manifolds, 28/03/2023, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 21 Mar '23

21 Mar '23

Title: Model order reduction of parametric Hamiltonian systems on matrix manifolds, Speaker(s): Cecilia Pagliantini, University of Pisa, Date and time: 28 Mar 2023, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/176 Abstract -------- 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 systems is challenged by several factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the slowly decaying Kolmogorov n-width of transport-dominated and non-dissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations; and (iii) nonlinear operators require hyper-reduction techniques that preserve the gradient structure of the flow velocity.We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to adapt in time an approximate low-dimensional phase space endowed with the geometric structure of the full model and to ensure that the reduced flow is still Hamiltonian. -- Indico :: Email Notifier https://events.dm.unipi.it/e/176

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[Indico] Prof. Lloyd N. Trefethen, Applications of AAA Rational Approximation, 21/02/2023, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 20 Feb '23

20 Feb '23

Title: Applications of AAA Rational Approximation, Speaker(s): Prof. Lloyd N. Trefethen, Mathematical Institute, University of Oxford, Date and time: 21 Feb 2023, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Volterra). Address: Piazza dei Cavalieri, 7 - 56126 Pisa You can access the full event here: https://events.dm.unipi.it/e/158 Abstract -------- Abstract: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 then demonstrate a number of applications, includingdetection of singularities, model order reduction, analytic continuation, functions of matrices, nonlinear eigenvalue problems, interpolation of equispaced data, smooth extension of multivariate real functions, extrapolation of ODE and PDE solutions into the complex plane, solution of Laplace problems, conformal mapping, Wiener-Hopf factorization. Note ---- A reminder of tomorrow's seminar. -- Indico :: Email Notifier https://events.dm.unipi.it/e/158

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[Indico] Prof. Lloyd N. Trefethen, Applications of AAA Rational Approximation, 21/02/2023, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 13 Feb '23

13 Feb '23

Title: Applications of AAA Rational Approximation, Speaker(s): Prof. Lloyd N. Trefethen, Mathematical Institute, University of Oxford, Date and time: 21 Feb 2023, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Volterra). Address: Piazza dei Cavalieri, 7 - 56126 Pisa You can access the full event here: https://events.dm.unipi.it/e/158 Abstract -------- Abstract: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 then demonstrate a number of applications, includingdetection of singularities, model order reduction, analytic continuation, functions of matrices, nonlinear eigenvalue problems, interpolation of equispaced data, smooth extension of multivariate real functions, extrapolation of ODE and PDE solutions into the complex plane, solution of Laplace problems, conformal mapping, Wiener-Hopf factorization. -- Indico :: Email Notifier https://events.dm.unipi.it/e/158

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Colloquio De Giorgi - Volker Mehrmann, Dirac and Lagrange structures in energy-based mathematical modeling 24/02/23, 16:00
by Fabio Durastante 01 Feb '23

01 Feb '23

We apologize in advance for cross-posting. ******************************************************************************** CENTRO DI RICERCA MATEMATICA "ENNIO DE GIORGI" ******************************************************************************** COLLOQUIO DE GIORGI Centro De Giorgi, Pisa, 24th February 2023 Aula Dini: 4.00 pm The event will take place in person. Volker Mehrmann Technische Universität Berlin Title:“Dirac and Lagrange structures in energy-based mathematical modeling” Abstract: 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. To deal with such complex system, in recent years the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very successful modeling methodology. The main reasons are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserve the pH structure and the physical properties are encoded in the geometric properties of the flow as well as the algebraic properties of the equations. Furthermore, dissipative pH system form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability analysis. Using global geometric and algebraic points of view, via Dirac and Lagrange spaces or manifolds, translations between different representations are presented. Characterizations are also derived when a general differential-algebraic system can be transformed into one of these structured representations. Numerical approaches for computing the structural information and the described transformations are derived and the results are demonstrated with some real world examples. Web site: http://www.crm.sns.it/course/6529/ <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230131222506106602…> Please note that for organizational purposes, registration <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230131222506106602…>is mandatory. CRM Secretariat Scuola Normale Superiore Piazza dei Cavalieri, 3 56126 Pisa, Italy

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[Indico] Dr Gianluca Ceruti, Robust numerical integrators for dynamical low-rank approximation, 15/12/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 14 Dec '22

14 Dec '22

Title: Robust numerical integrators for dynamical low-rank approximation, Speaker(s): Dr Gianluca Ceruti, École Polytechnique Fédérale de Lausanne, Date and time: 15 Dec 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: room Aula Magna (Dipartimento di Matematica). You can access the full event here: https://events.dm.unipi.it/e/138 Abstract -------- 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 devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, we present a broad overview on dynamical low-rank approximation together with recent developments on robust numerical integrators for it. Dynamical low-rank approximation for matrices is firstly presented, and a numerical integrator with two remarkable properties is introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. Then, via a novel compact formulation of the Tucker integrator, we further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given by (but not only restricted to) Tensor Trains.The present seminar is based upon joint works with Ch. Lubich, H. Walach, J. Kusch, and D. Sulz. -- Indico :: Email Notifier https://events.dm.unipi.it/e/138

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[Indico] Dr Gianluca Ceruti, Robust numerical integrators for dynamical low-rank approximation, 15/12/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 12 Dec '22

12 Dec '22

Title: Robust numerical integrators for dynamical low-rank approximation, Speaker(s): Dr Gianluca Ceruti, École Polytechnique Fédérale de Lausanne, Date and time: 15 Dec 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: room Aula Riunioni (Dipartimento di Matematica). You can access the full event here: https://events.dm.unipi.it/e/138 Abstract -------- 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 devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, we present a broad overview on dynamical low-rank approximation together with recent developments on robust numerical integrators for it. Dynamical low-rank approximation for matrices is firstly presented, and a numerical integrator with two remarkable properties is introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. Then, via a novel compact formulation of the Tucker integrator, we further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given by (but not only restricted to) Tensor Trains.The present seminar is based upon joint works with Ch. Lubich, H. Walach, J. Kusch, and D. Sulz. -- Indico :: Email Notifier https://events.dm.unipi.it/e/138

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Assegno di ricerca presso il Dipartimento di Matematica
by Leonardo Robol 23 Nov '22

23 Nov '22

Buongiorno, si è appena aperto un bando per un assegno di ricerca di 12 mesi presso il Dipartimento di Matematica (di Pisa), su fondi PNRR. La scadenza è il 21/12/22. Vi prego diffondere l'annuncio con chiunque possa essere interessato/a. https://bandi.unipi.it/public/Bandi/Detail/f2d456ca-5df1-4fcd-b95c-d16d0434…. A presto, -- Leonardo Robol.

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[Indico] Aaron Melman, Recent extensions of scalar and matrix polynomial properties and their interactions, 10/11/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 03 Nov '22

03 Nov '22

Title: Recent extensions of scalar and matrix polynomial properties and their interactions, Speaker(s): Aaron Melman, Santa Clara University, USA, Date and time: 10 Nov 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/114 Abstract -------- 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 magnitudes of polynomial zeros or eigenvalues having a given argument, as well as results involving real polynomials with sign restrictions on their coefficients. The latter lead to exclusion sectorsfor polynomial eigenvalues. In addition, it is shown how new results can be obtained by embedding scalar polynomials into a matrix polynomial framework, and examples are given of how the interactionbetween scalar and matrix polynomials benefits both. If time (and interest) permits, an improvement of theorems by Hayashi and Hurwitz from the beginning of the twentiethcentury will be presented. These theorems concern the location of polynomial zeros when the coefficients exhibit certain sign patterns. -- Indico :: Email Notifier https://events.dm.unipi.it/e/114

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