Due Giorni di Algebra Lineare Numerica e Applicazioni

Geometric means of more than two matrix sequences in the case of hidden (asymptotic) structures

20 Jan 2025, 16:00

2h

Building E (Aula Magna "Fratelli Pontecorvo", Building E, Polo Fibonacci. Pisa)

Poster Poster Session

Speaker

Muhammad Faisal Khan

Description

We consider the spectral distribution of the geometric mean of two or more Hermitian positive definite (HPD) matrix-sequences, under the assumption that all input matrix-sequences belong to the same Generalized Locally Toeplitz (GLT) $*$-algebra. As expected, the numerical experiments show that the geometric mean of $k$ positive definite GLT matrix-sequences forms a new GLT matrix-sequence, with the GLT symbol given by the geometric mean of the individual symbols. While the result is plain for $k=2$, it is highly non trivial for $k>2$, due to the limit process for defining the geometrc mean and due to the lack of a closed form expression. Theoretical tools for handling the difficult case are discussed.

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6. M.F. Khan, S. Serra-Capizzano, Geometric means of more than two matrix-sequences in the case of hidden (asymptotic) structures, preprint 2024.