@TechReport{ it:2014-022,
author = {Carlo Garoni and Stefano Serra-Capizzano and Paris
Vassalos},
title = {Tools for Determining the Asymptotic Spectral Distribution
of {H}ermitian Matrix-Sequences and Applications},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2014},
number = {2014-022},
month = dec,
abstract = {We consider sequences of Hermitian matrices with
increasing dimension, and we provide a general tool for
deducing the asymptotic spectral distribution of a
`difficult' sequence $\{A_n\}_n$, starting from the one of
`simpler' sequences $\{B_{n,m}\}_n$ that approximate
$\{A_n\}_n$ when $m\to\infty$. The tool is based on the
notion of approximating class of sequences (a.c.s.), which
was inspired by the work of Paolo Tilli and the second
author, and is applied here in a more general setting. An
a.c.s.-based proof of the famous Szego theorem on the
spectral distribution of Toeplitz matrices is finally presented.}
}