Electronic structure calculations which are based on Wannier, like loc
alized orbitals or the related density matrix, are an alternative to c
onventional calculations based on extended orbitals. For large systems
this approach is potentially faster since it offers O(N) scaling with
respect to the number of atoms in the system. We derive a class of al
gorithms based on projection to calculate either the localized orbital
s or the density matrix. (c) 1995 Academic Press, Inc.