An extension of the theory of GLT sequences: sampling on asymptotically uniform grids

Giovanni Barbarino, Carlo Garoni*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
33 Downloads (Pure)

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 languageEnglish
Pages (from-to)2008-2025
Number of pages18
JournalLINEAR AND MULTILINEAR ALGEBRA
Volume71
Issue number12
Early online date30 Jun 2022
DOIs
Publication statusPublished - 2023
MoE publication typeA1 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

Fingerprint

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.

Cite this