Projects per year
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 |
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Pages (from-to) | 2008-2025 |
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 article-refereed |
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
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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