Options
Gershgorin-type spectral inclusions for matrices
Citation Link: https://doi.org/10.15480/882.16304
Publikationstyp
Journal Article
Date Issued
2025-11-26
Sprache
English
TORE-DOI
Volume
732
Start Page
33
End Page
73
Citation
Linear Algebra and its Applications 732: 33-73 (2026)
Publisher DOI
Scopus ID
Publisher
Elsevier
In this paper we derive sequences of Gershgorin-type inclusion sets for the spectra and pseudospectra of finite matrices. In common with previous generalisations of the classical Gershgorin bound for the spectrum, our inclusion sets are based on a block decomposition. In contrast to previous generalisations that treat the matrix as a perturbation of a block-diagonal submatrix, our arguments treat the matrix as a perturbation of a block-tridiagonal matrix, which can lead to sharp spectral bounds, as we show for the example of large Toeplitz matrices. Our inclusion sets, which take the form of unions of pseudospectra of square or rectangular submatrices, build on our own recent work on inclusion sets for bi-infinite matrices in Chandler-Wilde et al. (2024)
DDC Class
510: Mathematics
515: Analysis
Publication version
publishedVersion
Loading...
Name
1-s2.0-S0024379525004768-main.pdf
Size
2.2 MB
Format
Adobe PDF