Convergence of Hill's Method for Nonselfadjoint Operators
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Issue Date
2012-01-01Author
Johnson, Mathew A.
Zumbrun, Kevin
Publisher
Society for Industrial and Applied Mathematics
Type
Article
Article Version
Scholarly/refereed, publisher version
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By the introduction of a generalized Evans function defined by an appropriate 2-modified Fredholm determinant, we give a simple proof of convergence in location and multiplicity of Hill's method for numerical approximation of spectra of periodic-coefficient ordinary differential operators. Our results apply to operators of nondegenerate type under the condition that the principal coefficient matrix be symmetric positive definite (automatically satisfied in the scalar case). Notably, this includes a large class of non-self-adjoint operators which previously had not been treated in a simple way. The case of general coefficients depends on an interesting operator-theoretic question regarding properties of Toeplitz matrices.
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This is the published version, also available here: http://dx.doi.org/10.1137/100809349.
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Citation
Johnson, Mathew A. & Zumburn, Kevin "Convergence of Hill's Method for Nonselfadjoint Operators." SIAM J. Numer. Anal., 50(1), 64–78. (15 pages). http://dx.doi.org/10.1137/100809349.
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