NumPI July 2017

numpi@lists.dm.unipi.it

2 participants
2 discussions

Optimization & Numerical Analysis seminars: Iannazzo
by Federico Poloni 26 Jul '17

26 Jul '17

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 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
by Dario A. Bini 11 Jul '17

11 Jul '17

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 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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NumPI July 2017