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Convergence of Hill's Method for Nonselfadjoint Operators
Johnson, Mathew A. Zumbrun, Kevin
Johnson, Mathew A.
Zumbrun, Kevin
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Abstract
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.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/100809349.
Date
2012-01-01
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Society for Industrial and Applied Mathematics
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Keywords
Hill's Method, periodic-coefficient operators, Floquet-Bloch decomposition, Fredholm determinant, Evans function
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.