Convergent spectral inclusion sets for banded matrices

Simon N. Chandler-Wilde; Ratchanikorn Chonchaiya; Marko Lindner

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arXiv · 2306.11138

Convergent spectral inclusion sets for banded matrices

Simon N. Chandler-Wilde·Ratchanikorn Chonchaiya·Marko Lindner

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Abstract

We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain submatrices of a chosen size $n$. Via the choice of $n$, one can balance accuracy of approximation against computational cost, and we show, in the case of infinite matrices, convergence as $n\to\infty$ of the respective inclusion set to the corresponding spectral set.

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BibTeX RIS

Simon N. Chandler-Wilde, Ratchanikorn Chonchaiya, Marko Lindner. 2023-06-19. Convergent spectral inclusion sets for banded matrices. https://arxiv.org/abs/2306.11138

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