Speaker: Bruno Iannazzo
Affiliation: Università di Perugia, Italy
Time: Thursday 2017-08-27, h. 11:00
Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa
Title: The Riemannian Barzilai-Borwein algorithm and the matrix
geometric mean
computation
Abstract:
We consider the problem of computing the geometric mean of positive
definite matrices, the so-called Karcher mean.
For this purpose, we adapt the Barzilai-Borwein method from nonlinear
optimization to Riemannian manifold …
[View More]optimization. Incomporating a
nonmonotone line-search strategy yields global convergence under
standard assumptions, fulfilled in the problem of the matrix geometric mean.
By a set of numerical tests, we show that the Riemannian
Barzilai-Borwein method notably outperforms existing first-order
optimization methods for computing the matrix geometric mean.
===
Everyone is welcome. Sorry for the short notice!
--
--federico poloni
Dipartimento di Informatica, Università di Pisa
http://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143
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Avviso di Seminario:
Speaker: Rajendra Bhatia
Affiliation: Indian Statistical Institute, Delhi
Date: July 11
Time: 11:00 -- 12:00
Place: Aula Magna
Title: The Bures-Wasserstein distance on positive definite matrices
Abstract:
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 …
[View More]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.
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