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IMA Journal of Numerical Analysis Advance Access published online on August 27, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drp013
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Quadratic projection methods for approximating the spectrum of self-adjoint operators

Michael Strauss{dagger}

Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK

{dagger} Corresponding author. Email: ra.mstr{at}maths.strath.ac.uk

Received on 13 February 2008. Revised on 18 February 2009.


  Abstract

The pollution-free approximation of the spectrum for self-adjoint operators using a quadratic projection method has recently been studied. Higher-order pollution-free approximation can be achieved by combining this technique with a method due to Kato. To illustrate, an example from magnetohydrodynamics is considered. Whether or not this procedure converges to the whole spectrum is unknown. Combining the quadratic method with the Galerkin method, we derive procedures that do converge to the whole spectrum and without pollution.

Key Words: quadratic projection methods; second-order relative spectrum; spectral pollution


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