Approximation of pseudospectra on a Hilbert space

Publikationstyp
Conference Paper
Date Issued
2016-06-08
Sprache
English
Author(s)
Schmidt, Torge  
Lindner, Marko  orcid-logo
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/6249
Volume
1738
Article Number
480050
Citation
AIP Conference (1738): 480050 (2016-06-08)
Contribution to Conference
AIP conference 2016  
Publisher DOI
10.1063/1.4952286
Scopus ID
2-s2.0-84984576626
The study of spectral properties of linear operators on an infinite-dimensional Hilbert space is of great interest. This task is especially difficult when the operator is non-selfadjoint or even non-normal. Standard approaches like spectral approximation by finite sections generally fail in that case. In this talk we present an algorithm which rigorously computes upper and lower bounds for the spectrum and pseudospectrum of such operators using finite-dimensional approximations. One of our main fields of research is an efficient implementation of this algorithm. To this end we will demonstrate and evaluate methods for the computation of the pseudospectrum of finite-dimensional operators based on continuation techniques.
Subjects
Hilbert Space
Operator Theory
Pseudospectra