We present a method for phonon spectrum calculations from electronic s
tructure calculations that scales linearly with system size. It allows
computation of the dynamical matrix and phonon structure of systems o
f unprecedented size. The method is based on (i) use of localized wave
functions to describe the electronic states, (ii) truncation of the d
ynamical matrix beyond a cutoff, and (iii) reconstruction of the spect
rum of the sparse dynamical matrix by the maximum entropy approach of
Drabold and Sankey. We test the method with a tight-binding Hamiltonia
n for carbon, on a 216 atom supercell in the diamond structure, and in
fullerene balls of up to 3840 atoms.