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[NOMADS] Seminar - Matthew Colbrook - Dec 1 at 17:00
by Francesco Tudisco 29 Nov '21

29 Nov '21

Dear all, We are starting this week a new series of NOMADS seminars on Numerical methods, Matrix analysis and Data Science. This week's seminar will take place on *Wednesday December 1 at 17:00* (CET) in the *GSSI Main Lecture Hall* (the "red" conference hall by the entrance of the lecture rooms building). The speaker is Matthew J Colbrook from University of Cambridge and ENS Paris, with a talk on the computation of semigroups of fractional PDEs. Title and abstract are below. In person participation is encouraged, but remote attendance will also be possible via the link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Hope to see you all on Wednesday! And, please feel free to distribute this announcement as you see fit. Francesco and Nicola ----------- Title: Computing semigroups and time-fractional PDEs with error control Abstract: We develop an algorithm that computes strongly continuous semigroups on infinite-dimensional Hilbert spaces with explicit error control. Given a generator $A$, a time $t > 0$, an arbitrary initial vector $u_0$ and an error tolerance $\epsilon > 0$, the algorithm computes $\exp(tA)u_0$ with error bounded by $\epsilon$. The (parallelisable) algorithm is based on a combination of a regularized functional calculus, suitable contour quadrature rules and the adaptive computation of resolvents in infinite dimensions. As a particular case, we deal with semigroups on $L^2(R^d)$ that are generated by partial differential operators with polynomially bounded coefficients of locally bounded total variation. For analytic semigroups, we provide a quadrature rule whose error decreases like $\exp(−cN/ log(N))$ for $N$ quadrature points, that remains stable as $N \to \infty$, and which is also suitable for infinite-dimensional operators. Finally, we extend the method to time-fractional PDEs (where it avoids singularities as $t \to 0$ and large memory consumption). Numerical examples are given, including: Schrödinger and wave equations on the aperiodic Ammann–Beenker tiling and fractional beam equations arising in the modelling of small-amplitude vibration of viscoelastic materials. The spectral analysis (which is always needed for contour methods) is considerably simplified due to an infinite-dimensional “solve-then-discretise” approach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/CAO2_FWmWATOjsjz5v5…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Annuncio di seminario, 19/11 (Mariarosa Mazza)
by Leonardo Robol 18 Nov '21

18 Nov '21

Speaker: Mariarosa Mazza Affiliation: Università dell'Insubria Venue: Aula Magna, Dipartimento di Matematica Time: Venerdì, 19/11/2021, 10:00 Title: Caputo and Riemann-Liouville fractional derivatives: a matrix comparison Fractional derivatives are a mathematical tool that received much attention in the last decades because of their non-local behavior which has been demonstrated to be useful when modeling anomalous diffusion phenomena appearing, e.g., in imaging or electrophysiology. Two of the most famous definitions of fractional derivatives are the Riemann- Liouville and the Caputo ones. The two formulations are related by a well-known formula that expresses a Riemann-Liouville derivative as a Caputo one plus a term that depends on the function and its derivatives at the boundary. As a consequence of this relation, Riemann-Liouville and Caputo derivatives coincide only for sufficiently smooth functions that satisfy homogeneous conditions at the boundary. Aiming at uncovering how much this discrepancy reflects on their discretized counterparts, we focus on the relation between Riemann-Liouville and Caputo derivatives once approximated by a collocation method based on B-splines, i.e., high order finite elements with maximum regularity. We show that when the fractional order α ranges in (1,2) their difference in terms of matrices corresponds to a rank-1 correction whose spectral norm increases with the mesh-size n and is o(√n). On one hand, this implies that the spectral distribution for the B-spline collocation matrices corresponding to the Riemann-Liouville and Caputo derivatives coincide; on the other hand, the presence of the rank-1 correction makes the Caputo matrices worse conditioned for α tending to 1 due to a larger maximum singular value. Some linear algebra consequences of all this knowledge are discussed, and a selection of numerical experiments that validate our findings is provided together with a numerical study of the approximation behavior of B-spline collocation. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario, 25/10 (Cecilia Pagliantini)
by Leonardo Robol 25 Oct '21

25 Oct '21

Speaker: Cecilia Pagliantini Affiliation: TU Eindhoven Venue: Sala Seminari, Dipartimento di Matematica Time: Monday, 25/10/2021, 15:00 Title: Structure-preserving dynamical model order reduction of parametric Hamiltonian systems 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 techniques aim at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. In this talk, we will consider reduced basis methods (RBM) for the model order reduction of parametric Hamiltonian dynamical systems describing nondissipative phenomena. The development of RBM for Hamiltonian systems is challenged by two main 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 \emph{local} low-rank nature of transport-dominated and nondissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations. 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 evolve low-dimensional surrogate models on a phase space that adapts in time while being endowed with the geometric structure of the full model. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario, 15/10 (Igor Simunec)
by Leonardo Robol 15 Oct '21

15 Oct '21

Cari tutti, a breve ricominceremo con i tradizionali seminari NumPi, questa volta in forma "ibrida". Per tutti quelli che vorranno ci sarà la possibilità di seguire in presenza in Aula Magna del Dipartimento di Matematica (compilando questa form: https://forms.gle/AaMgajhKhroXdHqY6) Per gli altri, organizzeremo lo streaming tramite il solito link ( https://hausdorff.dm.unipi.it/b/leo-xik-xu4) Qui sotto trovate l'annuncio del primo seminario; a breve vi farò avere un Doodle per provare a scegliere un giorno che torni il più comodo possibile a tutti, da utilizzare per quelli successivi. Trovate tutte le informazioni sulla pagina dei seminari del sito NumPi (https://numpi.dm.unipi.it/seminars) A presto, -- Leonardo. Speaker: Igor Simunec Affiliation: Scuola Normale Superiore, Pisa Time: Friday, 15/10/2021, 16:30 Title: Computation of generalized matrix functions with rational Krylov methods 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 decomposition. In this talk, we consider the computation of the action of a generalized matrix function on a vector and we present a class of algorithms based on rational Krylov methods [2]. These algorithms incorporate as a special case previous methods based on the Golub-Kahan bidiagonalization [1]. By exploiting the quasiseparable structure of the projected matrices, we show that the basis vectors can be updated using a short recurrence, which can be seen as a generalization to the rational case of the Golub-Kahan bidiagonalization. We also prove error bounds that relate the error of these methods to uniform rational approximation on an interval containing the singular values of the matrix. The effectiveness of the algorithms and the accuracy of the bounds is illustrated with numerical experiments. This is joint work with Angelo A. Casulli (Scuola Normale Superiore). [1] F. Arrigo, M. Benzi, and C. Fenu, Computation of generalized matrix functions, SIAM J. Matrix Anal. Appl. 37 (2016), no. 3, 836–860. [2] A. A. Casulli, I. Simunec, Computation of generalized matrix functions with rational Krylov methods, arXiv:2107.12074 (2021). [3] J. B. Hawkins and A. Ben-Israel, On generalized matrix functions, Linear and Multilinear Algebra 1 (1973), no. 2, 163–171. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Orario per seminari NumPi
by Leonardo Robol 13 Oct '21

13 Oct '21

Cari tutti, a partire dal prossimo seminario (dopo quello di Igor venerdì) cercheremo di scegliere un orario compatibile con gli impegni di tutti, e mantere una cadenza indicativamente bisettimanale. Ho creato un Doodle [1] per la settimana 25/10 - 29/10, dove chiederei (a chi è interessato a seguire i seminari in presenza e/o online) di indicare le preferenze di orario. Sebbene il Doodle sia per quella settimana specifica, è da intendersi come le preferenze in base ai vostri impegni settimanali. Vi chiederei di farci avere una risposta entro venerdì, così che possiamo organizzare il seminario seguente basandoci sulle risposte. Grazie! A presto, -- Leonardo (e Fabio). [1] https://doodle.com/poll/dtvyu6uakv3exdp8

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PhD position in Prague
by Leonardo Robol 12 Aug '21

12 Aug '21

Cari tutti, inoltro un messaggio da Stefano Pozza, su una borsa di dottorato disponibile alla Charles University, Praga. Trovate i dettagli in fondo alla mail. Buone vacanze, -- Leonardo. ----------------------------------------------------------------------- Ph.D. Position, Dep Num Math, Charles Univ, Czech Rep A Ph.D. position is available within the framework of the Primus Research Programme: "A Lanczos-like Method for the Time-Ordered Exponential" at the Faculty of Mathematics and Physics, Charles University, Prague. The four years of Ph.D. studies will take place in the Department of Numerical Mathematics under the supervision of Dr. Stefano Pozza (PI of the project). The department offers an international environment at one of the top universities in the Czech Republic, and the oldest university in Central Europe. The student will also have the opportunity to work with external collaborators from France, Italy, and the UK. The applicants must hold a Master's degree by the start date of Spring 2022 (to be announced) and have a strong interest in numerical linear algebra and numerical analysis. Knowledge of Matlab or other programming languages is necessary. Applicants will have to prove their English language level by passing an exam (it is possible to waive the examination under some conditions). Application deadline: September 30, 2021. More information and application instructions: https://www.starlanczos.cz/open-positions

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Cena NumPi
by Leonardo Robol 30 Jun '21

30 Jun '21

Cari tutti, come gli anni scorsi (ed in particolare quelli non-pandemici), vorremmo provare ad organizzare una cena di "fine seminari"; più che altro sarebbe una scusa per vedersi, a maggior ragione quest'anno dove non ci siamo (quasi) mai incontrati di persona. Ho predisposto un Doodle dove potete segnare la vostra disponibilità, se intendete partecipare: https://doodle.com/poll/z2xw2k6u5zzfybn3 Siete tutti benvenuti (dagli ordinari ai dottorandi, ma anche simpatizzanti, ecc.). Vi chiederei solo di segnare la vostra presenza quanto prima così che riusciamo ad organizzarci per bene. Il luogo non è stato ancora scelto, ma proposte sono sempre bene accette; probabilmente dovremo scegliere anche in funzione del numero di partecipanti. A presto! -- Leonardo Robol.

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Reminder: Seminar today (Stefano Cipolla)
by Fabio Durastante 18 Jun '21

18 Jun '21

Speaker: Stefano Cipolla Affiliation: University of Edinburgh Time: Friday, 18/06/2021, 16:00 Title: Random multi-block ADMM: an ALM based view for the QP case Because of its wide versatility and applicability in multiple fields, the n-block alternating direction method of multipliers (ADMM) for solving nonseparable convex minimization problems, has recently attracted the attention of many researchers [1, 2, 4]. When the n-block ADMM is used for the minimization of quadratic functions, it consists in a cyclic update of the primal variables xi for i = 1,...,n in the Gauss-Seidel fashion and a dual ascent type update of the dual variable μ. Despite the fact the connections between ADMM and Gauss-Seidel are quite well known, to the best of our knowledge, an analysis from the purely numerical linear algebra point of view is lacking in literature. Aim of this talk is to present a series of very recent results obtained on this topic which shed further light on basic issues as convergence and efficiency [3]. [1] Chen, C., Li, M., Liu, X., Ye, Y. (2019). Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights. Mathematical Programming, 173(1-2), 37-77. [2] Chen, C., He, B., Ye, Y., Yuan, X. (2016). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1-2), 57-79. [3] Cipolla, S., Gondzio, J (2020). ADMM and inexact ALM: the QP case. arXiv 2012.09230. [4] Sun, R., Luo, Z. Q., Ye, Y. (2020). On the efficiency of random permutation for ADMM and coordinate descent. Mathematics of Operations Research, 45(1), 233-271. https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base… <https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base…> Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 <https://hausdorff.dm.unipi.it/b/leo-xik-xu4>

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Colloquium on 16/06 at 5pm (Volker Mehrmann)
by Paola Boito 16 Jun '21

16 Jun '21

Dear all, An online colloquium of the Department of Mathematics at UniPi is planned on June 16 at 17:00. You are all welcome! The speaker is Volker Mehrmann (TU Berlin). Title: Energy based modeling, simulation, and control. Mathematical theory and algorithms for the solution of real world problems. Abstract: Energy based modeling via port-Hamiltonian systems is a relatively new paradigm in all areas of science and engineering. These systems have wonderful mathematical properties, concerning their analytic, geometric and algebraic properties, but also with respect to their use in numerical algorithms for space-time discretization, model reduction and control. We will introduce the model class and their mathematical properties and we illustrate their usefulness with several real world applications. Google Meet link: https://meet.google.com/qii-tcks-rrr

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Seminar on 18/06 (Stefano Cipolla)
by Leonardo Robol 14 Jun '21

14 Jun '21

Speaker: Stefano Cipolla Affiliation: University of Edinburgh Time: Friday, 18/06/2021, 16:00 Title: Random multi-block ADMM: an ALM based view for the QP case Because of its wide versatility and applicability in multiple fields, the n-block alternating direction method of multipliers (ADMM) for solving nonseparable convex minimization problems, has recently attracted the attention of many researchers [1, 2, 4]. When the n-block ADMM is used for the minimization of quadratic functions, it consists in a cyclic update of the primal variables xi for i = 1,...,n in the Gauss-Seidel fashion and a dual ascent type update of the dual variable μ. Despite the fact the connections between ADMM and Gauss-Seidel are quite well known, to the best of our knowledge, an analysis from the purely numerical linear algebra point of view is lacking in literature. Aim of this talk is to present a series of very recent results obtained on this topic which shed further light on basic issues as convergence and efficiency [3]. [1] Chen, C., Li, M., Liu, X., Ye, Y. (2019). Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: convergence analysis and insights. Mathematical Programming, 173(1-2), 37-77. [2] Chen, C., He, B., Ye, Y., Yuan, X. (2016). The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent. Mathematical Programming, 155(1-2), 57-79. [3] Cipolla, S., Gondzio, J (2020). ADMM and inexact ALM: the QP case. arXiv 2012.09230. [4] Sun, R., Luo, Z. Q., Ye, Y. (2020). On the efficiency of random permutation for ADMM and coordinate descent. Mathematics of Operations Research, 45(1), 233-271. https://www.dm.unipi.it/webnew/it/seminari/random-multi-block-admm-alm-base… Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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