An extension of the theory of GLT sequences

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2023
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
LINEAR AND MULTILINEAR ALGEBRA
Abstract
The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic singular value and spectral distributions of matrices (Formula presented.) arising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices (Formula presented.) give rise to a sequence (Formula presented.), which often turns out to be a GLT sequence. In this paper, we provide an extension of the theory of GLT sequences: we show that any sequence of diagonal sampling matrices constructed from asymptotically uniform samples of an almost everywhere continuous function falls in the class of GLT sequences. We also detail a few representative applications of this result in the context of finite difference discretizations of DEs with discontinuous coefficients.
Description
Publisher Copyright: © 2022 Informa UK Limited, trading as Taylor & Francis Group.
Keywords
15A18, 15B05, 47B06, 65N06, asymptotically uniform grids, discretization of differential equations, finite differences, Generalized locally Toeplitz sequences, singular value and spectral distributions
Other note
Citation
Barbarino , G & Garoni , C 2023 , ' An extension of the theory of GLT sequences : sampling on asymptotically uniform grids ' , LINEAR AND MULTILINEAR ALGEBRA , vol. 71 , no. 12 , pp. 2008-2025 . https://doi.org/10.1080/03081087.2022.2092585