Order-N method to calculate the local density of states

We present a rigorous and general method to extract the local density of states r i(v) of a system from its time response to a specified external perturbation. This method is order-N when the matrix is sparse. In a single run it gives r i(v),r i(2v), . . . ,r i(nv), . . . concurrently, which enhances the total efficiency by two decades. Application to a lattice-dynamics problem of 4096 SiC particles in a supercell with a dynamical matrix generated from an appropriate interatomic potential shows excellent agreement with exact phonon-dispersion calculations; the accelerated algorithm yields a full local density of states spectrum for each supercell k point in 15 min on a desktop workstation. Results showing the effects of an antisite-pair defect are given for which methods requiring lattice periodicity cannot be used. @S0163-1829~97!06932-4#