Chandler-Wilde, Simon N.Simon N.Chandler-WildeChonchaiya, RatchanikornRatchanikornChonchaiyaLindner, MarkoMarkoLindner2023-10-252023-10-252023-12Proceedings in applied mathematics and mechanics 23 (4): e202300016 (2023-12)https://hdl.handle.net/11420/43822We 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 as 𝑛 →∞ of the respective inclusion set to the corresponding spectral set.en1617-706120234Wiley-VCHhttps://creativecommons.org/licenses/by-nc-nd/4.0/MathematicsJournal Article10.15480/882.950110.1002/pamm.20230001610.15480/882.9501Journal Article