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

Strauss, M. (2011) Quadratic projection methods for approximating the spectrum of self-adjoint operators. IMA Journal of Numerical Analysis, 31 (1). pp. 40-60. ISSN 0272-4979

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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.

Item type: Article
ID code: 40448
Keywords: second-order relative spectrum, quadratic projection methods, pollution, eigenvalues, pseudospectra, spectral pollution, relative spectra, Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics, Mathematics(all)
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
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Depositing user: Pure Administrator
Date Deposited: 17 Jul 2012 16:25
Last modified: 27 Mar 2014 10:17
URI: http://strathprints.strath.ac.uk/id/eprint/40448

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