SEMINARI DI ANALISI NUMERICA

On classical, extended, and rational Krylov and the associated QR algorithms

Relatore: 
Raf Vandebril

In this lecture we will discuss three main classes of Krylov and QR type methods: the
classical, the extended, and the rational versions. We will initially focus on the
classical QR method and reintepret all ingredients such as: associated Krylov spaces,
associated Hessenberg matrices, implicit theorems, bulge chasing, eigenvalue swapping, and
subspace iteration.  Another look at these essentials will allow us to straightforwardly
generalize all of this to the extended and rational case.

Data Seminario: 
Friday, April 6, 2018
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
KU Leuven
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Optimal Interpolation Formulas in W_2^{(m,m-1)} space

Relatore: 
Samandar Babaev

In this talk, using S.L.Sobolev’s method, optimal interpolation formulas are constructed in W_{2} ^(m,m1) (0,1) space. Explicit formulas for coefficients of optimal interpolation formulas are obtained. Some numerical results are presented.

Data Seminario: 
Wednesday, November 8, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
Bukhara State University, Uzbekistan
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Counting Fiedler pencils using diagrams

Fiedler pencils are a family of matrix pencils which generalizes the
well-known companion matrix: they are *linearizations*, i.e., they
provide a method to construct, given a matrix polynomial, a linear
eigenvalue problem with the same eigenvalues and multiplicities.

Fiedler pencils are constructed as products of special block matrices
that act nontrivially only on two contiguous blocks. They have a rich
structure that give rise to many combinatorial properties.

Data Seminario: 
Tuesday, October 31, 2017
Relatore: 
Federico Poloni
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
Dipartimento di Informatica, Universita' di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Backward error analysis for polynomial rootfinders

Relatore: 
Leonardo Robol

The most common methods to compute roots of polynomials is to rephrase the problem in linear algebra terms: one constructs a companion matrix (or pencil) that has the roots of the polynomial as eigenvalues.
However, even when the eigenvalue method used is backward stable, it's non-trivial to map the backward error back on the polynomial. This problem has been studied extensively in the past and it has been shown that relying on the QR method does not provide a normwise backward-stable rootfinder. For this reason, one needs to rely on QZ + appropriate scaling.

Data Seminario: 
Tuesday, October 17, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
ISTI--CNR Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

The Bures-Wasserstein distance on positive definite matrices

Relatore: 
Rajendra Bhatia

We will discuss an interesting metric on the space of positive definite matrices, called the Bures distance in the quantum information literature and the Wasserstein metric in optimal transport. This has connections with Riemannian geometry, statistics, QIT and optimal transport. We will explain these connections. The two-variable and several-variable mean with respect to this metric will be described. Our perspective from matrix analysis leads to simpler proofs and suggests new problems. 

Data Seminario: 
Tuesday, July 11, 2017
Aula: 
Aula Magna (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
Indian Statistical Institute, Delhi
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Numerical Analysis Seminar - Tensor Analysis: Spectral Theory and Special Tensors

Relatore: 
Liqun Qi

Abstract:

Data Seminario: 
Monday, June 12, 2017
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
The Hong Kong Polytechnic University, Department of Applied Mathematics
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Optimization & Numerical Analysis seminars. Algoritmi adattivi per il Clustering convesso e non convesso basato sulla NMF simmetrica

Abstract: Vengono presentati algoritmi adattivi basati sulla
fattorizzazione simmetrica non negativa di matrici sia per il caso di
cluster con inviluppo convesso che di cluster qualsiasi. A parte il
calcolo delle distanze tra i punti, gli algoritmi non fanno uso di
nozioni geometriche.

Lavoro congiunto con Paola Favati (CNR), Grazia Lotti (Università di
Parma), Ornella Menchi

http://pages.di.unipi.it/fpoloni/files/seminari/romani.doc
 

Data Seminario: 
Monday, June 20, 2016
Relatore: 
Francesco Romani - Scuola Normale Superiore di Pisa
Ora Fine: 
Saturday, January 1, 0000 - 10:00
Affiliazione: 
Il seminario si svolgerà presso la Sala Seminari Ovest, Dipartimento di Informatica, Universitàdi Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 09:00

Numerical Analysis and Optimization Seminars - Spettri, Matrici e Applicazioni nella Approssimazione di Equazioni alle Derivate Parziali.

Relatore: 
Stefano Serra Capizzano

Abstract:
La presentazione è volta ad illustrare come dedurre informazioni sullo spettro di matrici provenienti dalla approssimazione numerica di equazioni alle derivate parziali: il secondo passo, di interesse
squisitamente numerico, consiste nell’impiegare l'informazione ottenuta per il 'design' di metodi efficienti per il calcolo della soluzione dei risultanti sistemi lineari di grandi dimensioni.
La chiacchierata, molto informale, includerà una breve discussione su alcuni problemi applicativi.

Data Seminario: 
Monday, May 30, 2016
Aula: 
Sala Riunioni (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:30
Affiliazione: 
Università dell'Insubria
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Optimization & Numerical Analysis seminars. Numerical quasiseparable preservation in matrix functions and in the cyclic reduction.

Abstract: The quasiseparable structure can be efficiently exploited - in order to speed up computations and storage - by using hierachical
representations. This theme has raised much interest in the last two
decades, in particular in the context of elliptic partial differential
equations, matrix functions and Sylvester equations. Our aim is to
provide a framework for the analysis of the off-diagonal singular
values, focusing on the structures that can ensure an exponential decay of them.

Data Seminario: 
Thursday, May 5, 2016
Relatore: 
Stefano Massei - Scuola Normale Superiore di Pisa
Ora Fine: 
Saturday, January 1, 0000 - 10:00
Affiliazione: 
Il Seminario si svolgerà nella Sala Seminari Est, Dipartimento Informatica. Università di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 09:00

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