Lanczos algorithm and energy-weighted sum rules for linear response Original Research Article

An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes 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 Np as O(Np3).