Spectral Pollution
By E. Davies, Michael Plum. 2003
104 citations recorded by the source corpus.
Unfortunately one often encounters the problem of spectral pollution: the matrix may possess eigenvalues which are unrelated to any spectral properties of the original operator. This is an important problem in several areas of applied mathematics, as is illustrated by recent papers, [1, 2, 3, 4, 5, 10, 16, 17, 20]. There are methods of detecting and resolving such problems, but they are not easy to understand and for that reason are not well appreciated. Our main result in this paper is the proof that, at least in some situations, the geometrically motivated method of Davies, [7] is mathematically equivalent to the method of Zimmermann and Mertins, [20] which is based on Lehmann’s method [14] and its extension by Goerisch [1]. We also provide various other ideas and examples to motivate the method and show how well it works.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ac7c91a2b52c64700559f2509e3ca7bf94926ccf
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- On the approximation of spectra of linear operators on Hilbert spaces (2008, background): “In fact γn can be used alone to estimate σ(A) and that has been investigated in [15].”
- On the Solvability Complexity Index, the n-pseudospectrum and approximations of spectra of operators (2011, background): “For selected papers and books we consider to be important and related to the topic of this paper we refer to [9, 11, 10, 26, 32, 15, 14, 41, 19, 18, 28, 42, 47] for a functional analysis exposition and [50, 48, 25, 39] for a more applied mathematical treatment.”