  In the framework of a recently reported linear-scaling method for
density-functional-pseudopotential calculations, we investigate the use of
localized basis functions for such work. We propose a basis set in which each
local orbital is represented in terms of an array of `blip functions'' on the
points of a grid. We analyze the relation between blip-function basis sets and
the plane-wave basis used in standard pseudopotential methods, derive criteria
for the approximate equivalence of the two, and describe practical tests of
these criteria. Techniques are presented for using blip-function basis sets in
linear-scaling calculations, and numerical tests of these techniques are
reported for Si crystal using both local and non-local pseudopotentials. We
find rapid convergence of the total energy to the values given by standard
plane-wave calculations as the radius of the linear-scaling localized orbitals
is increased.
