Comparison of quadrature and termination for estimating the density of states within the recursion method

Within the recursion method, the local density of states is estimated from a truncated continued fraction (Jacobi matrix). For simple one- and two-band models, the authors compare the two methods for calculating the density of states. The quadrature method assumes no information other than the truncated fraction. Given exact band edges in addition to the truncated fraction, an analytic terminator can do better than quadrature if the internal singularities are sufficiently weak.