  We propose a distinct numerical approach to effectively solve the problem of
partial diagonalization of the super-large-scale quantum electronic Hamiltonian
matrices. The key ingredients of our scheme are the new method for arranging
the basis vectors in the computer's RAM and the algorithm allowing not to store
a matrix in RAM, but to regenerate it on-the-fly during diagonalization
procedure. This scheme was implemented in the program, solving the Anderson
impurity model in the framework of dynamical mean-field theory (DMFT). The DMFT
equations for electronic Hamiltonian with 18 effective orbitals that
corresponds to the matrix with the dimension of 2.4 * 10^9 were solved on the
distributed memory computational cluster.
