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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

On the Solvability Complexity Index, the $ n$-pseudospectrum and approximations of spectra of operators


Author: Anders C. Hansen
Journal: J. Amer. Math. Soc. 24 (2011), 81-124
MSC (2010): Primary 47A10; Secondary 47A75, 46L05, 81Q10, 81Q12, 65J10
Published electronically: July 12, 2010
MathSciNet review: 2726600
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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.


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Additional Information

Anders C. Hansen
Affiliation: Department of Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
Email: A.Hansen@damtp.cam.ac.uk

DOI: http://dx.doi.org/10.1090/S0894-0347-2010-00676-5
PII: S 0894-0347(2010)00676-5
Received by editor(s): August 28, 2009
Published electronically: July 12, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.