A linear prediction of the recursion coefficients

A technique is presented to extrapolate the recursion coefficients from a knowledge of the first few. In the linear prediction theory, the coefficients of the continued fraction are written as sums of complex exponentials. The exponential decays and amplitudes are obtained by a least-squares fit to the first known coefficients. This procedure allows the determination of the band limits which are generally not known in the recursion method. The author shows that they are in good agreement with the exact ones. This method also notably improves the continued-fraction expansion of the density of states. An application is made to the calculation of the bulk Si and GaAs electronic densities of states.