The forced oscillator method: eigenvalue analysis and computing linear response functions

A review is given of the forced oscillator method (FOM), an algorithm particularly suitable to treat physical systems described by very large matrices. This scheme enables us to compute spectral densities, eigenvalues and their eigenvectors of both Hermitian and non-Hermitian matrices with high speed and accuracy, in particular when combined with the fast time-evolution method based on the Chebyshev polynomial expansion. In addition, linear response functions can be computed with high speed and accuracy in the context of the FOM. The emphasis will be on the presentation of the efficiency of the FOM for a broad range of applications with their computer source codes for the purpose of wide utility.