A systematic approach to reduced GLT

Giovanni Barbarino*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)
35 Downloads (Pure)


This paper concerns the spectral analysis of matrix-sequences that are generated by the discretization and numerical approximation of partial differential equations, in case the domain is a generic Peano–Jordan measurable set. It is observed that such matrix-sequences often present a spectral symbol, that is a measurable function describing the asymptotic behaviour of the eigenvalues. When the domain is a hypercube, the analysis can be conducted using the theory of generalized locally Toeplitz (GLT) sequences, but in case of generic domains, a different kind of matrix-sequences and theory has to be formalized. We thus develop in full detail the theory of reduced GLT sequences and symbols, presenting some application to finite differences and finite elements discretization for linear convection–diffusion–reaction differential equations.

Original languageEnglish
Pages (from-to)681 - 743
Number of pages63
JournalBIT Numerical Mathematics
Issue number3
Early online date14 Sept 2021
Publication statusPublished - Sept 2022
MoE publication typeA1 Journal article-refereed


  • Algebra of sequences
  • Asymptotic distribution of singular values and eigenvalues
  • Discretization of PDE on general domain
  • Finite differences
  • Finite elements
  • Multilevel generalized locally Toeplitz sequence


Dive into the research topics of 'A systematic approach to reduced GLT'. Together they form a unique fingerprint.

Cite this