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 part...
