Hill's method for computing spectra of linear operators

Hill's method is a method for the computation of spectra of linear operators. The method is ideally suited for spectra of operators with periodic coefficients in 1,2, or 3 dimensions. Further, the method is easily extended to problems defined on the whole real line, plane or space. The method is spectrally convergent due to the use of Fourier series or transforms. Incorporating Floquet theory allows for the computation of the entire spectrum, as opposed to a few elements of it.