Spectral pollution
Copyright policy )Spectral pollution
We discuss the problems arising when computing eigenvalues of self-adjoint operators which lie in a gap between two parts of the essential spectrum. Spectral pollution, i.e. the apparent existence of eigenvalues in numerical computations, when no such eigenvalues actually exist, is commonplace in problems arising in applied mathematics. We describe a geometrically inspired method which avoids this difficulty, and show that it yields the same results as an algorithm of Zimmermann and Mertins.
23 pages
- Kings College London, University of London United Kingdom
- King's College London United Kingdom
- Karlsruhe Institute of Technology Germany
ddc:510, numerical examples, spectral pollution, self-adjoint operator, Hilbert space, spurious eigenvalues, 510, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Numerical solutions to equations with linear operators, 47A75, FOS: Mathematics, 49R50, Spectrum, resolvent, 35P05, Spectral Theory (math.SP), Mathematics, info:eu-repo/classification/ddc/510, 35P15;35P05;47A75;49R50, 35P15, Analysis of PDEs (math.AP)
ddc:510, numerical examples, spectral pollution, self-adjoint operator, Hilbert space, spurious eigenvalues, 510, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Numerical solutions to equations with linear operators, 47A75, FOS: Mathematics, 49R50, Spectrum, resolvent, 35P05, Spectral Theory (math.SP), Mathematics, info:eu-repo/classification/ddc/510, 35P15;35P05;47A75;49R50, 35P15, Analysis of PDEs (math.AP)
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