  We propose a practicable method for describing linear dynamics of different
finite Fermi systems. The method is based on a general self-consistent
procedure for factorization of the two-body residual interaction. It is
relevant for diverse density- and current-dependent functionals and, in fact,
represents the self-consistent separable random-phase approximation (RPA),
hence the name SRPA. SRPA allows to avoid diagonalization of high-rank RPA
matrices and thus dwarfs the calculation expense. Besides, SRPA expressions
have a transparent analytical form and so the method is very convenient for the
analysis and treatment of the obtained results. SRPA demonstrates high
numerical accuracy. It is very general and can be applied to diverse systems.
Two very different cases, the Kohn-Sham functional for atomic clusters and
Skyrme functional for atomic nuclei, are considered in detail as particular
examples. SRPA treats both time-even and time-odd dynamical variables and, in
this connection, we discuss the origin and properties of time-odd currents and
densities in initial functionals. Finally, SRPA is compared with other
self-consistent approaches for the excited states, including the
coupled-cluster method.
