  We present an efficient preconditioning technique for accelerating the fixed
point iteration in real-space Kohn-Sham density functional theory (DFT)
calculations. The preconditioner uses a low rank approximation of the
dielectric matrix (LRDM) based on G\^ateaux derivatives of the residual of
fixed point iteration along appropriately chosen direction functions. We
develop a computationally efficient method to evaluate these G\^ateaux
derivatives in conjunction with the Chebyshev filtered subspace iteration
procedure, an approach widely used in large-scale Kohn-Sham DFT calculations.
Further, we propose a variant of LRDM preconditioner based on adaptive
accumulation of low-rank approximations from previous SCF iterations, and also
extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We
demonstrate the robustness and efficiency of the LRDM preconditioner against
other widely used preconditioners on a range of benchmark systems with sizes
ranging from $\sim$ 100-1100 atoms ($\sim$ 500--20,000 electrons). The
benchmark systems include various combinations of
metal-insulating-semiconducting heterogeneous material systems, nanoparticles
with localized $d$ orbitals near the Fermi energy, nanofilm with metal dopants,
and magnetic systems. In all benchmark systems, the LRDM preconditioner
converges robustly within 20--30 iterations. In contrast, other widely used
preconditioners show slow convergence in many cases, as well as divergence of
the fixed point iteration in some cases. Finally, we demonstrate the
computational efficiency afforded by the LRDM method, with up to 3.4$\times$
reduction in computational cost for the total ground-state calculation compared
to other preconditioners.
