We present a comparison of real-space methods based on regular grids for electronic structure calculations that are designed to have basis set variational properties, using as a reference the conventional method of finite differences ~a real-space method that is not variational! and the reciprocal-space plane-wave method which is fully variational. We find that a definition of the finite-differ...

Anecessary and sufficient condition for a weighted composite difference operator to be bounded is investigated in this paper. The adjoint of obtained.