TY - JOUR
T1 - Complexity issues in computing spectra, pseudospectra and resolvents
AU - Hansen, Anders C
AU - Nevanlinna, Olavi
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
U2 - 10.4064/bc112-0-10
DO - 10.4064/bc112-0-10
M3 - Article
VL - 112
JO - BANACH CENTER PUBLICATIONS
T2 - BANACH CENTER PUBLICATIONS
JF - BANACH CENTER PUBLICATIONS
SN - 0137-6934
ER -