@TechReport{ it:2018-009,
author = {Carlo Garoni and Mariarosa Mazza and Stefano
Serra-Capizzano},
title = {Block Generalized Locally Toeplitz Sequences: From the
Theory to the Applications},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2018},
number = {2018-009},
month = may,
abstract = {The theory of generalized locally Toeplitz (GLT) sequences
is a powerful apparatus for computing the asymptotic
spectral distribution of matrices $A_n$ arising from
virtually any kind of numerical discretization of
differential equations (DEs). Indeed, when the mesh
fineness parameter $n$ tends to infinity, these matrices
$A_n$ give rise to a sequence $\{A_n\}_n$, which often
turns out to be a GLT sequence or one of its ``relatives'',
i.e., a block GLT sequence or a reduced GLT sequence. In
particular, block GLT sequences are encountered in the
discretization of systems of DEs as well as in the
higher-order finite element or discontinuous Galerkin
approximation of scalar DEs. Despite the applicative
interest, a solid theory of block GLT sequences has been
developed only recently, in 2018. The purpose of the
present paper is to illustrate the potential of this theory
by presenting a few noteworthy examples of applications in
the context of DE discretizations.}
}