The method has two variants. In the first one (denoted as MCFV) we construct approximations of the potential energy operator V in the form of separable function of rank 1, 2, 3... The second variant (MCFG method) constructs the finite rank approximations to Green's operator. The approximations are constructed within Krylov subspace constructed from vector | ϕ ϕ ⟩ ⟩ with action of the operator A = G 0 V . The method can thus be understood as resummation of (in general divergent) Born series by Padé approximants. It is also closely related to Schwinger variational principle. In general the method requires similar amount of numerical work as calculation of terms of Born series, but it provides much faster convergence of the results.