Complexity issues in computing spectra, pseudospectra and resolvents

Anders C Hansen, Olavi Nevanlinna

Research output: Contribution to journalArticleScientificpeer-review


We display methods that allow for computations of spectra, pseudospectra and resolvents of linear operators on Hilbert spaces and also elements in unital Banach algebras. The paper considers two different approaches, namely, pseudospectral techniques and polynomial numerical hull theory. The former is used for Hilbert space operators whereas the latter can handle the general case of elements in a Banach algebra. This approach leads to multicentric holomorphic calculus. We also discuss some new types of pseudospectra and the recently defined Solvability Complexity Index.
Original languageEnglish
Number of pages22
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed


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