A simple, stable, and rapid procedure for the calculation of modified moments and continued fraction coefficients for the diatomic linear chain is presented. The Chebyshev modified moments are obtained stably from a simple threehyphen;term recursion relation. Stable determination of the continued fraction coefficients requires a more sophisticated approach, also based on threehyphen;term recursion relations. This procedure also allows stable calculation of the continued fraction coefficients for more complex model densities with singularities within the bands. Examples are given and the corresponding behavior of the continued fraction coefficients is discussed.
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