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

Hansen, Anders^1, 2

¹ Department of Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125
² Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

Journal of the American Mathematical Society, Tome 24 (2011) no. 1, pp. 81-124

Résumé

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.

Détail

DOI : 10.1090/S0894-0347-2010-00676-5

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