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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The second order spectrum and optimal convergence


Author: Michael Strauss
Journal: Math. Comp. 82 (2013), 2305-2325
MSC (2010): Primary 47A75, 47B15
Published electronically: April 9, 2013
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Abstract: The method of second order relative spectra has been shown to reliably approximate the discrete spectrum for a self-adjoint operator. We extend the method to normal operators and find optimal convergence rates for eigenvalues and eigenspaces. The convergence to eigenspaces is new, while the convergence rate for eigenvalues improves on the previous estimate by an order of magnitude.


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Additional Information

Michael Strauss
Affiliation: School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, Wales, United Kingdom CF24 4AG
Email: straussmd@cardiff.ac.uk

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02693-2
PII: S 0025-5718(2013)02693-2
Keywords: Spectral pollution, second order relative spectrum, convergence to eigenvalues, convergence to eigenvectors, projection methods, finite-section method
Received by editor(s): May 10, 2011
Received by editor(s) in revised form: June 13, 2011, and February 28, 2012
Published electronically: April 9, 2013
Additional Notes: The author gratefully acknowledges the support of EPSRC grant no. EP/I00761X/1.
Article copyright: © Copyright 2013 American Mathematical Society