Block Generalized Locally Toeplitz Sequences: From the Theory to the Applications
Institute of Computational Science, University of Italian Switzerland, 6900 Lugano, Switzerland
Department of Science and High Technology, University of Insubria, 22100 Como, Italy
Division of Numerical Methods in Plasma Physics, Max Planck Institute for Plasma Physics, 85748 Garching bei München, Germany
Department of Information Technology, Uppsala University, P.O. Box 337, SE-751 05 Uppsala, Sweden
Author to whom correspondence should be addressed.
Received: 9 May 2018 / Revised: 6 July 2018 / Accepted: 16 July 2018 / Published: 19 July 2018
The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices
arising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n
tends to infinity, these matrices
give rise to a sequence
, 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.
This is an open access article distributed under the Creative Commons Attribution License
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Garoni, C.; Mazza, M.; Serra-Capizzano, S. Block Generalized Locally Toeplitz Sequences: From the Theory to the Applications. Axioms 2018, 7, 49.
Garoni C, Mazza M, Serra-Capizzano S. Block Generalized Locally Toeplitz Sequences: From the Theory to the Applications. Axioms. 2018; 7(3):49.
Garoni, Carlo; Mazza, Mariarosa; Serra-Capizzano, Stefano. 2018. "Block Generalized Locally Toeplitz Sequences: From the Theory to the Applications." Axioms 7, no. 3: 49.
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