Gershgorin-type spectral inclusions for matrices
Year: 2025
Type: article
Abstract: 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)].
Authors: Simon N. Chandler-Wilde, Marko Lindner
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,230
Funder: University of Reading
OpenAlex ID: W4416713879