Seminar Details
2015-11-10 (14:00) : Matrix geometric means
At Euler building (A002)
Organized by Mathematical Engineering
Speaker :
Bruno Iannazzo (Università di Perugia)
Abstract :
A pleasant activity in Matrix Analysis is to try and generalize concepts from scalars to matrices. In this perspective, it is understood the quest for the definition of a geometric mean of Hermitian positive definite matrices. After many imperfect attempts, the "right" definition has been unearthed using a differential geometry argument. The interest in the matrix geometric mean is not just theoretical, since this matrix function has great power in averaging and interpolating positive definite matrices and hence is well suited for modeling. Thus, there is the need of good algorithms for computing it. We will tell the long journey to the definition of matrix geometric mean, briefly describe some applications and focus on the numerical methods for computing these means. Finally, we will discuss some lines of research in this topic.