MATHICSE-GroupSusnjara, AnaKressner, Daniel2019-09-272019-09-272019-09-272018-01-1610.5075/epfl-MATHICSE-270780https://infoscience.epfl.ch/handle/20.500.14299/161630Based 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.text::working paper