{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T13:07:31Z","timestamp":1772370451952,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,7,19]],"date-time":"2018-07-19T00:00:00Z","timestamp":1531958400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009112","name":"Istituto Nazionale di Alta Matematica &quot;Francesco Severi&quot;","doi-asserted-by":"publisher","award":["PCOFUND-GA-2012-600198"],"award-info":[{"award-number":["PCOFUND-GA-2012-600198"]}],"id":[{"id":"10.13039\/100009112","id-type":"DOI","asserted-by":"publisher"}]},{"name":"INdAM - GNCS (Gruppo Nazionale per il Calcolo Scientifico)","award":["Grant Number Not Available"],"award-info":[{"award-number":["Grant Number Not Available"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices An arising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices An give rise to a sequence {An}n, which often turns out to be a GLT sequence or one of its \u201crelatives\u201d, 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.<\/jats:p>","DOI":"10.3390\/axioms7030049","type":"journal-article","created":{"date-parts":[[2018,7,20]],"date-time":"2018-07-20T02:10:11Z","timestamp":1532052611000},"page":"49","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Block Generalized Locally Toeplitz Sequences: From the Theory to the Applications"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9720-092X","authenticated-orcid":false,"given":"Carlo","family":"Garoni","sequence":"first","affiliation":[{"name":"Institute of Computational Science, University of Italian Switzerland, 6900 Lugano, Switzerland"},{"name":"Department of Science and High Technology, University of Insubria, 22100 Como, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8505-6788","authenticated-orcid":false,"given":"Mariarosa","family":"Mazza","sequence":"additional","affiliation":[{"name":"Division of Numerical Methods in Plasma Physics, Max Planck Institute for Plasma Physics, 85748 Garching bei M\u00fcnchen, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9477-109X","authenticated-orcid":false,"given":"Stefano","family":"Serra-Capizzano","sequence":"additional","affiliation":[{"name":"Department of Science and High Technology, University of Insubria, 22100 Como, Italy"},{"name":"Department of Information Technology, Uppsala University, P.O. Box 337, SE-751 05 Uppsala, Sweden"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0024-3795(97)10079-9","article-title":"Locally Toeplitz sequences: Spectral properties and applications","volume":"278","author":"Tilli","year":"1998","journal-title":"Linear Algebra Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF00319101","article-title":"On bilinear forms in Gaussian random variables and Toeplitz matrices","volume":"79","author":"Avram","year":"1988","journal-title":"Probab. Theory Relat. Fields"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"B\u00f6ttcher, A., and Grudsky, S.M. (2000). Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis, Birkh\u00e4user Verlag.","DOI":"10.1007\/978-93-86279-04-0"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"B\u00f6ttcher, A., and Grudsky, S.M. (2005). 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