CALCULATION OF DENSITIES OF STATES AND SPECTRAL FUNCTIONS BY CHEBYSHEV RECURSION AND MAXIMUM-ENTROPY

We present an efficient algorithm for calculating spectral properties of large sparse Hamiltonian matrices such as densities of states and s pectral functions. The combination of Chebyshev recursion and maximum entropy achieves high-energy resolution without significant roundoff e rror, machine precision, or numerical instability limitations. If cont rolled statistical or systematic errors an acceptable, CPU and memory requirements scale linearly in the number of states. The inference of spectral properties from moments is much better conditioned for Chebys hev moments than for power moments. We adapt concepts from the kernel polynomial method, a linear Chebyshev approximation with optimized Gib bs damping, to control the accuracy of Fourier integrals of positive n onanalytic functions. We compare thr performance of kernel polynomial and maximum entropy algorithms for an electronic structure example.