  A practical algorithm for many-electron systems based on the path-integral
renormalization group (PIRG) method is proposed in the real-space
finite-difference (RSFD) approach. The PIRG method, developed for investigating
strongly correlated electron systems, has been successfully applied to some
models such as Hubbard models. However, to apply this method to more realistic
systems of electrons with long-range Coulomb interactions within the RSFD
formalism, the one-body Green's function, which requires large computational
resources, is to be replaced with an alternative. For the same reason, an
efficient algorithm for computing the Fock matrix is needed. The newly proposed
algorithm is free of the one-body Green's function and enables us to compute
the Fock matrix efficiently. Our result shows a significant reduction in CPU
time and the possibility of using the present algorithm as a practical
numerical tool.
