Gershgorin-type spectral inclusions for matrices

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283 and Lindner, M. (2025) Gershgorin-type spectral inclusions for matrices. Linear Algebra and its Applications. ISSN 1873-1856 doi: 10.1016/j.laa.2025.11.017 (In Press)

Abstract/Summary

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 [Chandler-Wilde, Chonchaiya, Lindner, J. Spectr. Theory 14, 719-804 (2024)].

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/127238
Identification Number/DOI	10.1016/j.laa.2025.11.017
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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