@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.}
}