  Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham
[SIAM J. Sci. Comput., 35(3): A1325-A1349, 2013], we propose a new algorithm
for computing all the eigenvalues and eigenvectors of a symmetric banded
matrix. For this purpose, we combine our previous work on the fast computation
of spectral projectors in the so called HODLR format, with a novel technique
for extracting a basis for the range of such a HODLR matrix. The numerical
experiments demonstrate that our algorithm exhibits quasilinear complexity and
allows for conveniently dealing with large-scale matrices.
