A note on the spectral distribution of non-Hermitian block matrices with Toeplitz blocks
Andrea Adriani, Giacomo Tento
TL;DR
This paper investigates the spectral distribution of non-Hermitian block matrices with Toeplitz blocks using GLT sequences and geometric means, supported by numerical tests.
Contribution
It introduces a novel analysis approach combining geometric means and GLT theory for spectral distribution of such matrices.
Findings
Derived theoretical spectral distribution results.
Validated findings with numerical tests and visualizations.
Abstract
In the present paper, we are concerned with the study of the spectral distribution of matrix-sequences showing a non-Hermitian block structure with Toeplitz blocks. We use the notion of geometric mean of matrices and the theory of Generalized Locally Toeplitz (GLT) sequences to perform our analysis and produce some numerical tests and visualizations to confirm our theoretical derivations.
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