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Complexity issues in computing spectra, pseudospectra and resolvents

Volume 112 / 2017

Anders C. Hansen, Olavi Nevanlinna Banach Center Publications 112 (2017), 171-194 MSC: Primary 47A10; Secondary 47A75, 03D78, 65J10. DOI: 10.4064/bc112-0-10


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.


  • Anders C. HansenDAMTP
    Centre for Mathematical Sciences
    University of Cambridge
    Wilberforce Rd
    Cambridge CB3 0WA, United Kingdom
  • Olavi NevanlinnaDepartment of Mathematics and Systems Analysis
    Aalto University
    FI-00076 Aalto, Finland

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