Convergent spectral inclusion sets for banded matrices

06/19/2023

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by   Simon N. Chandler-Wilde, et al.

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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→∞ of the respective inclusion set to the corresponding spectral set.