SEMINARI DI ANALISI NUMERICA

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: 
0000 - 12:00
Affiliazione: 
Indian Statistical Institute, Delhi
Ora Inizio: 
0000 - 11:00

Newton's method as an unexpectedly efficient root finder

Abstract: Newton’s method is well known as a root finder locally near the roots. It is often “not recommended” as a global root finder because of its “chaotic” properties. We give a very efficient theoretical upper bound on its speed of convergence: all roots of a degree d polynomial can be found with accuracy eps in

O(d^2 log^4 d + d log|\log eps|)

Data Seminario: 
Friday, October 23, 2015
Relatore: 
Dierk Schleicher
Ora Fine: 
0000 - 11:00
Affiliazione: 
Jacobs University, Bremen, Germany
Ora Inizio: 
0000 - 10:00

Extending Pellet's theorem to matrix polynomials

Relatore: 
A. U. Thor

Pellet's theorem is extended to matrix polynomials of the kind $A(x)=\sum_{i=0}^n A_i x^i$, where $A_i$ are $m\times m$ matrices. The extension relies on a generalization of Rouch\'e theorem to analytic matrix valued functions.

Data Seminario: 
Thursday, June 26, 2014
Aula: 
Sala delle Riunioni (Dip. Matematica Applicata)
Ora Fine: 
0000 - 19:00
Affiliazione: 
Univeristy of Pisa
Ora Inizio: 
0000 - 18:00
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