A Lanczos algorithm for linear response

An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic accuracy of the basic mean-field approximation, avoiding the problem of solving very large matrices. For local interactions, the computational effort for the method scales with the number of particles N p as O ( N 3 p ).