Published January 2011
| Published
Journal Article
Open
On the Solvability Complexity Index, the n-pseudospectrum and approximations of spectra of operators
- Creators
- Hansen, Anders C.
Abstract
We show that it is possible to compute spectra and pseudospectra of linear operators on separable Hilbert spaces given their matrix elements. The core in the theory is pseudospectral analysis and in particular the n-pseudospectrum and the residual pseudospectrum. We also introduce a new classification tool for spectral problems, namely, the Solvability Complexity Index. This index is an indicator of the "difficultness" of different computational spectral problems.
Additional Information
© 2010 American Mathematical Society. Reverts to public domain 28 years from publication. Received by the editors August 28, 2009. Article electronically published on July 12, 2010. The author would like to thank Bill Arveson, Erik Bédos, Albrecht Böttcher, Brian Davies, Percy Deift, Weinan E, Arieh Iserles, Olavi Nevanlinna, Don Sarason, Barry Simon and Nick Trefethen for useful discussions and comments.Attached Files
Published - Hansen2011p12346J_Am_Math_Soc.pdf
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Hansen2011p12346J_Am_Math_Soc.pdf
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Additional details
- Eprint ID
- 21749
- Resolver ID
- CaltechAUTHORS:20110113-115856738
- Created
-
2011-01-14Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field
- Other Numbering System Name
- Publisher Item Identifier (PII)
- Other Numbering System Identifier
- S 0894-0347(2010)00676-5