Spectral Pollution

Details Spectral Pollution Spectral Pollution

2003-02-12

arxiv.org/abs/math/0302145v1

Mathematics

Spectral Theory

23 pages

Scientific paper

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.

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