@TechReport{	  it:2018-001,
  author	= {Carlo Garoni and Stefano Serra-Capizzano and Debora
		  Sesana},
  title		= {The Theory of Block Generalized Locally Toeplitz
		  Sequences},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2018},
  number	= {2018-001},
  month		= jan,
  note		= {Updated 2018-01-30.},
  abstract	= {The theory of generalized locally Toeplitz (GLT) sequences
		  is a powerful apparatus for computing the asymptotic
		  singular value and eigenvalue distribution of matrices
		  $A_n$ arising from virtually any kind of numerical
		  discretization of differential equations (DEs). Indeed,
		  when the discretization 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 importance, a solid theory of block GLT
		  sequences is still missing. The purpose of the present
		  paper is to develop this theory in a systematic way.}
}