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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.
Original language  English 

Pages (fromto)  20082025 
Number of pages  18 
Journal  LINEAR AND MULTILINEAR ALGEBRA 
Volume  71 
Issue number  12 
Early online date  30 Jun 2022 
DOIs  
Publication status  Published  2023 
MoE publication type  A1 Journal articlerefereed 
Keywords
 15A18
 15B05
 47B06
 65N06
 asymptotically uniform grids
 discretization of differential equations
 finite differences
 Generalized locally Toeplitz sequences
 singular value and spectral distributions
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Dive into the research topics of 'An extension of the theory of GLT sequences: sampling on asymptotically uniform grids'. Together they form a unique fingerprint.Projects
 1 Finished

Noferini_Vanni_AoF_Project: Noferini Vanni Academy Project
Noferini, V. (Principal investigator), Quintana Ponce, M. (Project Member), Barbarino, G. (Project Member), Wood, R. (Project Member) & Nyman, L. (Project Member)
01/09/2020 → 31/08/2024
Project: Academy of Finland: Other research funding