SpectrUW: A laboratory for the numerical exploration of spectra of linear operators
Mathematics and Computers in Simulation
Computing spectra of linear operators using the Floquet-Fourier-Hill method
Journal of Computational Physics
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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.