*Theory of Condensed Matter, Cavendish Laboratory, Madingley
Road, Cambridge, CB3 0HE, U.K.*

Linear-scaling electronic structure methods are essential for
calculations on large systems. Some of these approaches use a
*systematic* basis set, the completeness of which may be tuned
with an adjustable parameter similar to the energy cut-off of
plane-wave techniques. The search for the electronic ground state in
such methods suffers from an ill-conditioning which is related to the
kinetic contribution to the total energy and which results in
unacceptably slow convergence. We present a general preconditioning
scheme to overcome this ill-conditioning and implement it within our
own first-principles linear-scaling density functional theory method.
The scheme may be applied in either real-space or reciprocal-space
with equal success. The rate of convergence is improved by an order of
magnitude and is found to be almost independent of the size of the
basis.

PACS numbers: 71.15.-m; 31.15.-p